{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T01:05:15Z","timestamp":1777424715666,"version":"3.51.4"},"publisher-location":"Berlin, Heidelberg","reference-count":49,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642366741","type":"print"},{"value":"9783642366758","type":"electronic"}],"license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-36675-8_8","type":"book-chapter","created":{"date-parts":[[2013,2,28]],"date-time":"2013-02-28T19:04:22Z","timestamp":1362078262000},"page":"151-164","source":"Crossref","is-referenced-by-count":19,"title":["Loops with Abelian Inner Mapping Groups: An Application of Automated Deduction"],"prefix":"10.1007","author":[{"given":"Michael","family":"Kinyon","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert","family":"Veroff","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Petr","family":"Vojt\u011bchovsk\u00fd","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"8_CR1","volume-title":"Foundations of the Theory of Quasigroups and Loops","author":"V.D. Belousov","year":"1967","unstructured":"Belousov, V.D.: Foundations of the Theory of Quasigroups and Loops. Izdat. Nauka, Moscow (1967) (in Russian)"},{"key":"8_CR2","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1090\/S0002-9947-1946-0017288-3","volume":"60","author":"R.H. Bruck","year":"1946","unstructured":"Bruck, R.H.: Contributions to the theory of loops. Trans. Amer. Math. Soc.\u00a060, 245\u2013354 (1946)","journal-title":"Trans. Amer. Math. Soc."},{"key":"8_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-43119-1","volume-title":"A Survey of Binary Systems","author":"R.H. Bruck","year":"1971","unstructured":"Bruck, R.H.: A Survey of Binary Systems. Springer, Heidelberg (1971)"},{"key":"8_CR4","doi-asserted-by":"publisher","first-page":"858","DOI":"10.1016\/j.ejc.2005.12.002","volume":"28","author":"P. Cs\u00f6rg\u0151","year":"2007","unstructured":"Cs\u00f6rg\u0151, P.: Abelian inner mappings and nilpotency class greater than two. European J. Combin.\u00a028, 858\u2013867 (2007)","journal-title":"European J. Combin."},{"key":"8_CR5","doi-asserted-by":"publisher","first-page":"242","DOI":"10.1007\/BF03323028","volume":"47","author":"P. Cs\u00f6rg\u0151","year":"2005","unstructured":"Cs\u00f6rg\u0151, P., Dr\u00e1pal, A.: Left conjugacy closed loops of nilpotency class two. Results Math.\u00a047, 242\u2013265 (2005)","journal-title":"Results Math."},{"key":"8_CR6","first-page":"213","volume":"45","author":"P. Cs\u00f6rg\u0151","year":"2004","unstructured":"Cs\u00f6rg\u0151, P., Kepka, T.: On loops whose inner permutations commute. Comment. Math. Univ. Carolin.\u00a045, 213\u2013221 (2004)","journal-title":"Comment. Math. Univ. Carolin."},{"key":"8_CR7","unstructured":"Dr\u00e1pal, A., Kinyon, M.K.: Buchsteiner loops: associators and constructions. arXiv\/0812.0412"},{"key":"8_CR8","doi-asserted-by":"publisher","first-page":"1662","DOI":"10.1016\/j.ejc.2007.10.001","volume":"29","author":"A. Dr\u00e1pal","year":"2008","unstructured":"Dr\u00e1pal, A., Vojt\u011bchovsk\u00fd, P.: Explicit constructions of loops with commuting inner mappings. European J. Combin.\u00a029, 1662\u20131681 (2008)","journal-title":"European J. Combin."},{"key":"8_CR9","doi-asserted-by":"publisher","first-page":"254","DOI":"10.1112\/jlms\/s1-24.4.254","volume":"24","author":"T. Evans","year":"1949","unstructured":"Evans, T.: Homomorphisms of non-associative systems. J. London Math. Soc.\u00a024, 254\u2013260 (1949)","journal-title":"J. London Math. Soc."},{"key":"8_CR10","doi-asserted-by":"crossref","first-page":"187","DOI":"10.5486\/PMD.1969.16.1-4.26","volume":"16","author":"F. Fenyves","year":"1969","unstructured":"Fenyves, F.: Extra loops II. On loops with identities of Bol-Moufang type. Publ. Math. Debrecen\u00a016, 187\u2013192 (1969)","journal-title":"Publ. Math. Debrecen"},{"key":"8_CR11","unstructured":"The GAP Group: GAP \u2013 Groups, Algorithms, and Programming, Version 4.4.10 (2007), http:\/\/www.gap-system.org"},{"key":"8_CR12","doi-asserted-by":"crossref","unstructured":"Hullot, J.-M.: A catalogue of canonical term rewriting systems. Technical Report CSC 113, SRI International (1980)","DOI":"10.21236\/ADA087641"},{"key":"8_CR13","doi-asserted-by":"publisher","first-page":"857","DOI":"10.1080\/00927879808826169","volume":"26","author":"T. Kepka","year":"1998","unstructured":"Kepka, T.: On the abelian inner permutation groups of loops. Comm. Algebra\u00a026, 857\u2013861 (1998)","journal-title":"Comm. Algebra"},{"key":"8_CR14","first-page":"223","volume":"38","author":"T. Kepka","year":"1997","unstructured":"Kepka, T., Phillips, J.D.: Connected transversals to subnormal subgroups. Comment. Math. Univ. Carolin.\u00a038, 223\u2013230 (1997)","journal-title":"Comment. Math. Univ. Carolin."},{"key":"8_CR15","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1016\/j.jalgebra.2007.05.007","volume":"317","author":"T. Kepka","year":"2007","unstructured":"Kepka, T., Kinyon, M.K., Phillips, J.D.: The structure of F-quasigroups. J. Algebra\u00a0317, 435\u2013461 (2007)","journal-title":"J. Algebra"},{"key":"8_CR16","doi-asserted-by":"publisher","first-page":"619","DOI":"10.1090\/S0002-9939-01-06090-7","volume":"130","author":"M.K. Kinyon","year":"2002","unstructured":"Kinyon, M.K., Kunen, K., Phillips, J.D.: Every diassociative A-loop is Moufang. Proc. Amer. Math. Soc.\u00a0130, 619\u2013624 (2002)","journal-title":"Proc. Amer. Math. Soc."},{"key":"8_CR17","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1007\/s00012-002-8205-0","volume":"48","author":"M.K. Kinyon","year":"2002","unstructured":"Kinyon, M.K., Kunen, K., Phillips, J.D.: A generalization of Moufang and Steiner loops. Algebra Universalis\u00a048, 81\u2013101 (2002)","journal-title":"Algebra Universalis"},{"key":"8_CR18","doi-asserted-by":"publisher","first-page":"767","DOI":"10.1081\/AGB-120027928","volume":"32","author":"M.K. Kinyon","year":"2004","unstructured":"Kinyon, M.K., Kunen, K., Phillips, J.D.: Diassociativity in conjugacy closed loops. Comm. Algebra\u00a032, 767\u2013786 (2004)","journal-title":"Comm. Algebra"},{"key":"8_CR19","first-page":"39","volume":"12","author":"M.K. Kinyon","year":"2004","unstructured":"Kinyon, M.K., Kunen, K.: The structure of extra loops. Quasigroups and Related Systems\u00a012, 39\u201360 (2004)","journal-title":"Quasigroups and Related Systems"},{"key":"8_CR20","doi-asserted-by":"publisher","first-page":"679","DOI":"10.1016\/j.jalgebra.2006.01.034","volume":"304","author":"M.K. Kinyon","year":"2006","unstructured":"Kinyon, M.K., Kunen, K.: Power-associative, conjugacy closed loops. J. Algebra\u00a0304, 679\u2013711 (2006)","journal-title":"J. Algebra"},{"key":"8_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1142\/S0219498807001990","volume":"6","author":"M.K. Kinyon","year":"2007","unstructured":"Kinyon, M.K., Phillips, J.D., Vojt\u011bchovsk\u00fd, P.: C-loops: extensions and constructions. J. Algebra Appl.\u00a06, 1\u201320 (2007)","journal-title":"J. Algebra Appl."},{"key":"8_CR22","doi-asserted-by":"publisher","first-page":"2393","DOI":"10.1090\/S0002-9947-07-04391-7","volume":"360","author":"M.K. Kinyon","year":"2008","unstructured":"Kinyon, M.K., Phillips, J.D., Vojt\u011bchovsk\u00fd, P.: When is the commutant of a Bol loop a subloop? Trans. Amer. Math. Soc.\u00a0360, 2393\u20132408 (2008)","journal-title":"Math. Soc."},{"key":"8_CR23","doi-asserted-by":"crossref","unstructured":"Kinyon, M.K., Veroff, R., Vojt\u011bchovsk\u00fd, P.: Loops with abelian inner mapping groups: an application of automated deduction, Web support (2012), http:\/\/www.cs.unm.edu\/~veroff\/AIM_LC\/","DOI":"10.1007\/978-3-642-36675-8_8"},{"key":"8_CR24","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/B978-0-08-012975-4.50028-X","volume-title":"Proceedings of the Conference on Computational Problems in Abstract Algebras","author":"D.E. Knuth","year":"1970","unstructured":"Knuth, D.E., Bendix, P.B.: Simple word problems in universal algebras. In: Leech, J. (ed.) Proceedings of the Conference on Computational Problems in Abstract Algebras, pp. 263\u2013298. Pergamon Press, Oxford (1970)"},{"key":"8_CR25","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1006\/jabr.1996.0216","volume":"183","author":"K. Kunen","year":"1996","unstructured":"Kunen, K.: Moufang quasigroups. J. Algebra\u00a0183, 231\u2013234 (1996)","journal-title":"J. Algebra"},{"key":"8_CR26","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1006\/jabr.1996.0321","volume":"185","author":"K. Kunen","year":"1996","unstructured":"Kunen, K.: Quasigroups, loops, and associative laws. J. Algebra\u00a0185, 194\u2013204 (1996)","journal-title":"J. Algebra"},{"key":"8_CR27","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1080\/00927879808826147","volume":"26","author":"K. Kunen","year":"1998","unstructured":"Kunen, K.: Alternative loop rings. Comm. Algebra\u00a026, 557\u2013564 (1998)","journal-title":"Comm. Algebra"},{"key":"8_CR28","doi-asserted-by":"publisher","first-page":"694","DOI":"10.1006\/jabr.1999.8006","volume":"220","author":"K. Kunen","year":"1999","unstructured":"Kunen, K.: G-Loops and permutation groups. J. Algebra\u00a0220, 694\u2013708 (1999)","journal-title":"J. Algebra"},{"key":"8_CR29","doi-asserted-by":"publisher","first-page":"2889","DOI":"10.1090\/S0002-9947-00-02350-3","volume":"352","author":"K. Kunen","year":"2000","unstructured":"Kunen, K.: The structure of conjugacy closed loops. Trans. Amer. Math. Soc.\u00a0352, 2889\u20132911 (2000)","journal-title":"Trans. Amer. Math. Soc."},{"key":"8_CR30","doi-asserted-by":"crossref","unstructured":"McCune, W.: Otter 3.0 Reference Manual and Guide. Tech. Report ANL-94\/6, Argonne National Laboratory, Argonne, IL (1994), http:\/\/www.mcs.anl.gov\/AR\/otter\/","DOI":"10.2172\/10129052"},{"key":"8_CR31","unstructured":"McCune, W.: Prover9, version 2009-02A, http:\/\/www.cs.unm.edu\/~mccune\/prover9\/"},{"key":"8_CR32","unstructured":"Nagy, G., Vojt\u011bchovsk\u00fd, P.: LOOPS: Computing with quasigroups and loops in GAP \u2013 a GAP package, version 2.0.0 (2008), http:\/\/www.math.du.edu\/loops"},{"key":"8_CR33","doi-asserted-by":"publisher","first-page":"2177","DOI":"10.1016\/j.jpaa.2009.04.004","volume":"213","author":"G.P. Nagy","year":"2009","unstructured":"Nagy, G.P., Vojt\u011bchovsk\u00fd, P.: Moufang loops with commuting inner mappings. J. Pure Appl. Algebra\u00a0213, 2177\u20132186 (2009)","journal-title":"J. Pure Appl. Algebra"},{"key":"8_CR34","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1017\/S0004972708001093","volume":"79","author":"M. Niemenmaa","year":"2009","unstructured":"Niemenmaa, M.: Finite loops with nilpotent inner mapping groups are centrally nilpotent. Bull. Aust. Math. Soc.\u00a079, 109\u2013114 (2009)","journal-title":"Bull. Aust. Math. Soc."},{"key":"8_CR35","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1112\/blms\/24.4.343","volume":"24","author":"M. Niemenmaa","year":"1992","unstructured":"Niemenmaa, M., Kepka, T.: On connected transversals to abelian subgroups in finite groups. Bull. London Math. Soc.\u00a024, 343\u2013346 (1992)","journal-title":"Bull. London Math. Soc."},{"key":"8_CR36","first-page":"73","volume":"14","author":"J.D. Phillips","year":"2006","unstructured":"Phillips, J.D.: A short basis for the variety of WIP PACC-loops. Quasigroups Related Systems\u00a014, 73\u201380 (2006)","journal-title":"Quasigroups Related Systems"},{"key":"8_CR37","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1142\/S021949880900345X","volume":"8","author":"J.D. Phillips","year":"2009","unstructured":"Phillips, J.D.: The Moufang laws, global and local. J. Algebra Appl.\u00a08, 477\u2013492 (2009)","journal-title":"J. Algebra Appl."},{"key":"8_CR38","doi-asserted-by":"crossref","unstructured":"Phillips, J.D., Shcherbacov, V.A.: Cheban loops. J. Gen. Lie Theory Appl. 4, Art. ID G100501, 5 p. (2010)","DOI":"10.4303\/jglta\/G100501"},{"key":"8_CR39","doi-asserted-by":"crossref","first-page":"267","DOI":"10.3233\/AIC-2010-0460","volume":"23","author":"J.D. Phillips","year":"2010","unstructured":"Phillips, J.D., Stanovsk\u00fd, D.: Automated theorem proving in quasigroup and loop theory. AI Commun.\u00a023, 267\u2013283 (2010)","journal-title":"AI Commun."},{"key":"8_CR40","unstructured":"Phillips, J.D., Stanovsk\u00fd, D.: Bruck loops with abelian inner mapping groups. Comm. Alg. (to appear)"},{"key":"8_CR41","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/s00012-005-1941-1","volume":"54","author":"J.D. Phillips","year":"2005","unstructured":"Phillips, J.D., Vojt\u011bchovsk\u00fd, P.: The varieties of loops of Bol-Moufang type. Algebra Universalis\u00a054, 259\u2013271 (2005)","journal-title":"Algebra Universalis"},{"key":"8_CR42","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/j.jalgebra.2005.07.011","volume":"293","author":"J.D. Phillips","year":"2005","unstructured":"Phillips, J.D., Vojt\u011bchovsk\u00fd, P.: The varieties of quasigroups of Bol-Moufang type: an equational reasoning approach. J. Algebra\u00a0293, 17\u201333 (2005)","journal-title":"J. Algebra"},{"key":"8_CR43","doi-asserted-by":"crossref","first-page":"115","DOI":"10.5486\/PMD.2006.3187","volume":"68","author":"J.D. Phillips","year":"2006","unstructured":"Phillips, J.D., Vojt\u011bchovsk\u00fd, P.: C-loops: an introduction. Publ. Math. Debrecen\u00a068, 115\u2013137 (2006)","journal-title":"Publ. Math. Debrecen"},{"key":"8_CR44","first-page":"279","volume":"49","author":"J.D. Phillips","year":"2008","unstructured":"Phillips, J.D., Vojt\u011bchovsk\u00fd, P.: A scoop from groups: equational foundations for loops. Comment. Math. Univ. Carolin.\u00a049, 279\u2013290 (2008)","journal-title":"Comment. Math. Univ. Carolin."},{"key":"8_CR45","series-title":"Sigma Series in Pure Math.","volume-title":"Quasigroups and Loops: Introduction","author":"H.O. Pflugfelder","year":"1990","unstructured":"Pflugfelder, H.O.: Quasigroups and Loops: Introduction. Sigma Series in Pure Math., vol.\u00a08. Heldermann Verlag, Berlin (1990)"},{"key":"8_CR46","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4176-8","volume-title":"An Introduction to the Theory of Groups","author":"J.J. Rotman","year":"1995","unstructured":"Rotman, J.J.: An Introduction to the Theory of Groups, 4th edn. Springer, New York (1995)","edition":"4"},{"key":"8_CR47","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/BF00252178","volume":"16","author":"R. Veroff","year":"1996","unstructured":"Veroff, R.: Using hints to increase the effectiveness of an automated reasoning program: case studies. J. Automated Reasoning\u00a016, 223\u2013239 (1996)","journal-title":"J. Automated Reasoning"},{"key":"8_CR48","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1023\/A:1010639725972","volume":"27","author":"R. Veroff","year":"2001","unstructured":"Veroff, R.: Solving open questions and other challenge problems using proof sketches. J. Automated Reasoning\u00a027, 157\u2013174 (2001)","journal-title":"J. Automated Reasoning"},{"key":"8_CR49","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1006\/jsco.1996.0030","volume":"21","author":"H. Zhang","year":"1996","unstructured":"Zhang, H., Bonacina, M.P., Hsiang, J.: PSATO: a distributed propositional prover and its application to quasigroup problems. J. Symbolic Computation\u00a021, 543\u2013560 (1996)","journal-title":"J. Symbolic Computation"}],"container-title":["Lecture Notes in Computer Science","Automated Reasoning and Mathematics"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-36675-8_8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T20:30:17Z","timestamp":1688070617000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-36675-8_8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642366741","9783642366758"],"references-count":49,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-36675-8_8","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}