{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T11:51:00Z","timestamp":1771329060771,"version":"3.50.1"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2013,8]]},"abstract":"<jats:p> We construct, for the first time, various types of specific non-special finite p-groups having abelian automorphism group. More specifically, we construct groups G with abelian automorphism group such that \u03b3<jats:sub>2<\/jats:sub>(G) &lt; Z(G) &lt; \u03a6(G), where \u03b3<jats:sub>2<\/jats:sub>(G), Z(G) and \u03a6(G) denote the commutator subgroup, the center and the Frattini subgroup of G respectively. For a finite p-group G with elementary abelian automorphism group, we show that at least one of the following two conditions holds true: (i) Z(G) = \u03a6(G) is elementary abelian; (ii) \u03b3<jats:sub>2<\/jats:sub>(G) = \u03a6(G) is elementary abelian, where p is an odd prime. We construct examples to show the existence of groups G with elementary abelian automorphism group for which exactly one of the above two conditions holds true. <\/jats:p>","DOI":"10.1142\/s0218196713500161","type":"journal-article","created":{"date-parts":[[2013,4,23]],"date-time":"2013-04-23T07:27:44Z","timestamp":1366702064000},"page":"1063-1077","source":"Crossref","is-referenced-by-count":5,"title":["ON FINITE p-GROUPS WITH ABELIAN AUTOMORPHISM GROUP"],"prefix":"10.1142","volume":"23","author":[{"given":"VIVEK K.","family":"JAIN","sequence":"first","affiliation":[{"name":"Department of Mathematics, Central University of Bihar, Patna 800 014, India"}]},{"given":"PRADEEP K.","family":"RAI","sequence":"additional","affiliation":[{"name":"School of Mathematics, Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211019, India"}]},{"given":"MANOJ K.","family":"YADAV","sequence":"additional","affiliation":[{"name":"School of Mathematics, Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211019, India"}]}],"member":"219","published-online":{"date-parts":[[2013,8,21]]},"reference":[{"key":"rf1","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1215\/ijm\/1256067587","volume":"9","author":"Adney J. E.","year":"1965","journal-title":"Illinois J. Math."},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/s000130050215"},{"key":"rf3","volume-title":"Groups of Prime Power Order","volume":"2","author":"Berkovich Y.","year":"2008"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700033978"},{"key":"rf7","first-page":"121","volume":"94","author":"Hegarty P.","year":"1995","journal-title":"Rend. Sem. Mat. Univ. Padova"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01222792"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01238631"},{"key":"rf10","volume-title":"An Introduction to the Theory of Groups of Finite Order","author":"Hilton H.","year":"1908"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.2307\/1968020"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1080\/00927870500387804"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-011-0167-5"},{"key":"rf14","first-page":"53","volume":"5","author":"Jamali A.","year":"2002","journal-title":"J. Group Theory"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/BF01229715"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-008-1008-z"},{"key":"rf17","first-page":"124","volume":"43","author":"Miller G. A.","year":"1914","journal-title":"Mess. Math."},{"key":"rf18","first-page":"47","volume":"92","author":"Morigi M.","year":"1994","journal-title":"Rend. Sem. Mat. Univ. Padova"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1080\/00927879508825327"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1007\/BF01899435"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196713500161","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:55:26Z","timestamp":1565117726000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196713500161"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8]]},"references-count":18,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2013,8,21]]},"published-print":{"date-parts":[[2013,8]]}},"alternative-id":["10.1142\/S0218196713500161"],"URL":"https:\/\/doi.org\/10.1142\/s0218196713500161","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,8]]}}}