{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T00:06:06Z","timestamp":1767139566695,"version":"build-2238731810"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"5-6","license":[{"start":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T00:00:00Z","timestamp":1741737600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T00:00:00Z","timestamp":1741737600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100009411","name":"Universit\u00e9 Paris-Est Cr\u00e9teil","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100009411","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2025,7]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We develop the model theory of\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\omega $$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mi>\u03c9<\/mml:mi>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -stable K-loops and symmetric spaces. Continuing Poizat\u2019s seminal work, we notably establish an appropriate version of the indecomposability theorem and we adapt Lascar\u2019s analysis to this context.\n                  <\/jats:p>","DOI":"10.1007\/s00153-025-00967-4","type":"journal-article","created":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T07:52:08Z","timestamp":1741765928000},"page":"857-876","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Sym\u00e9trons et K-boucles $$\\omega $$-stables"],"prefix":"10.1007","volume":"64","author":[{"given":"Samuel","family":"Zamour","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,3,12]]},"reference":[{"key":"967_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-43119-1","volume-title":"A survey of binary systems","author":"RH Bruck","year":"1971","unstructured":"Bruck, R.H.: A survey of binary systems. Springer, Berlin (1971)"},{"key":"967_CR2","doi-asserted-by":"publisher","first-page":"308","DOI":"10.2307\/1969612","volume":"63","author":"Bruck et Paige","year":"1965","unstructured":"Bruck et Paige: Loops whose inner mappings are automorphisms. Ann. Math. 63, 308\u2013324 (1965)","journal-title":"Ann. Math."},{"key":"967_CR3","doi-asserted-by":"publisher","DOI":"10.1515\/9783110900583","volume-title":"Loops in group theory and Lie theory","author":"P Nagy","year":"2002","unstructured":"Nagy, P., Strambach, K.: Loops in group theory and Lie theory. De Gruyter, Berlin (2002)"},{"issue":"2","key":"967_CR4","doi-asserted-by":"publisher","first-page":"137","DOI":"10.2140\/mt.2023.2.137","volume":"2","author":"Clausen et Tent","year":"2023","unstructured":"Clausen et Tent: Mock hyperbolic reflection spaces and Frobenius groups of finite Morley rank. Model Theory 2(2), 137\u2013175 (2023)","journal-title":"Model Theory"},{"key":"967_CR5","first-page":"73","volume":"37","author":"W Kerby","year":"1972","unstructured":"Kerby, W., Wefelscheid, H.: Bemerkungen fiber Fastbereieheund seharf zweifaeh transitive Gruppen. Abhand. Math. Seminar. Univ. Hamburg 37, 73 (1972)","journal-title":"Abhand. Math. Seminar. Univ. Hamburg"},{"key":"967_CR6","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1007\/BF01844504","volume":"8","author":"Kerby et Wefelscheid","year":"1972","unstructured":"Kerby et Wefelscheid: Conditions of finiteness on sharply 2-transitive groups. Aequa. Math. 8, 287\u2013290 (1972)","journal-title":"Aequa. Math."},{"key":"967_CR7","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1016\/0021-8693(74)90043-X","volume":"28","author":"Kerby et Wefelscheid","year":"1974","unstructured":"Kerby et Wefelscheid: The maximal sub near-field of a near-domain. J. Algebra 28, 319\u2013325 (1974)","journal-title":"J. Algebra"},{"key":"967_CR8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139015417","volume-title":"A course in model theory","author":"K Tent","year":"2012","unstructured":"Tent, K., Ziegler, M.: A course in model theory. Cambridge University Press, Cambridge (2012)"},{"issue":"3","key":"967_CR9","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1090\/jams\/892","volume":"31","author":"E Fr\u00e9con","year":"2018","unstructured":"Fr\u00e9con, E.: Simple groups of Morley rank 3 are algebraic. J. Amer. Math. Soc. 31(3), 643\u2013659 (2018)","journal-title":"J. Amer. Math. Soc."},{"key":"967_CR10","doi-asserted-by":"publisher","first-page":"374","DOI":"10.1016\/0021-8693(64)90017-1","volume":"11","author":"G Glauberman","year":"1964","unstructured":"Glauberman, G.: On loops of odd order. J. Algebra 11, 374\u2013396 (1964)","journal-title":"J. Algebra"},{"key":"967_CR11","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1112\/S1461157010000173","volume":"14","author":"KW Johnson","year":"2011","unstructured":"Johnson, K.W., Kinyon, M.K., Nagy, G.P., Vojt\u011bchovsk\u00fd, P.: Searching for small simple automorphic loops. LMS J. Comput. Math. 14, 200\u20132013 (2011)","journal-title":"LMS J. Comput. Math."},{"key":"967_CR12","doi-asserted-by":"publisher","DOI":"10.1007\/b83276","volume-title":"Theory of K-loops","author":"H Kiechle","year":"2002","unstructured":"Kiechle, H.: Theory of K-loops. Springer, Berlin (2002)"},{"key":"967_CR13","unstructured":"Lascar, B.: La th\u00e9orie des mod\u00e8les en peu de maux. Cassini, (2009)"},{"key":"967_CR14","volume-title":"Symmetric spaces I","author":"O Loos","year":"1969","unstructured":"Loos, O.: Symmetric spaces I. Benjamin, New York (1969)"},{"key":"967_CR15","unstructured":"Poizat, B.: Groupes Stables. Une tentative de r\u00e9conciliation entre la G\u00e9om\u00e9trie Alg\u00e9brique et la Logique Math\u00e9matique. Nur Al-Mantiq Wal-Ma\u2019rifah, (1987)"},{"key":"967_CR16","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/j.jalgebra.2017.10.007","volume":"497","author":"B Poizat","year":"2018","unstructured":"Poizat, B.: Milieu et sym\u00e9trie, \u00e9tude de la convexit\u00e9 dans les groupes sans involutions. J. Algebra 497, 143\u2013163 (2018)","journal-title":"J. Algebra"},{"issue":"3","key":"967_CR17","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1017\/jsl.2021.36","volume":"86","author":"B Poizat","year":"2021","unstructured":"Poizat, B.: Sym\u00e9tries et transvections, principalement dans les groupes de rang de Morley fini sans involutions. J. Symbolic Logic 86(3), 965\u2013990 (2021)","journal-title":"J. Symbolic Logic"},{"key":"967_CR18","unstructured":"Poizat, B.: Br\u00e9viaire du sym\u00e9tron. (2023)"},{"issue":"2","key":"967_CR19","doi-asserted-by":"publisher","first-page":"479","DOI":"10.2140\/mt.2024.3.479","volume":"3","author":"B Poizat","year":"2024","unstructured":"Poizat, B.: La conjecture d\u2019Alg\u00e9bricit\u00e9, dans une perspective historique, et surtout mod\u00e8le-th\u00e9orique. Model Theory 3(2), 479\u2013504 (2024)","journal-title":"Model Theory"},{"key":"967_CR20","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511566080","volume-title":"Stable groups","author":"FO Wagner","year":"1997","unstructured":"Wagner, F.O.: Stable groups. Cambridge University Press, Cambridge (1997)"},{"key":"967_CR21","doi-asserted-by":"crossref","unstructured":"Zamour, S.: Etude des quasi-groupes de Frobenius et des K-boucles de rang de Morley fini. PhD thesis, Universit\u00e9 Lyon 1, (2022)","DOI":"10.2140\/mt.2023.2.69"}],"updated-by":[{"DOI":"10.1007\/s00153-025-00988-z","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T00:00:00Z","timestamp":1761177600000}}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-025-00967-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00153-025-00967-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-025-00967-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T05:36:45Z","timestamp":1761197805000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00153-025-00967-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,12]]},"references-count":21,"journal-issue":{"issue":"5-6","published-print":{"date-parts":[[2025,7]]}},"alternative-id":["967"],"URL":"https:\/\/doi.org\/10.1007\/s00153-025-00967-4","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"value":"0933-5846","type":"print"},{"value":"1432-0665","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,12]]},"assertion":[{"value":"1 February 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 February 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 March 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 October 2025","order":5,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Correction","order":6,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"A Correction to this paper has been published:","order":7,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"https:\/\/doi.org\/10.1007\/s00153-025-00988-z","URL":"https:\/\/doi.org\/10.1007\/s00153-025-00988-z","order":8,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interests"}}]}}