{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,30]],"date-time":"2024-07-30T07:12:48Z","timestamp":1722323568334},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2021,2]]},"abstract":"<jats:p>Let [Formula: see text] be an odd prime and let [Formula: see text], [Formula: see text] and [Formula: see text] denote the three different versions of Thompson subgroups for a [Formula: see text]-group [Formula: see text]. In this paper, we first prove an extension of Glauberman\u2019s replacement theorem [G. Glauberman, A characteristic subgroup of a p-stable group, Canad. J. Math. 20 (1968) 1101\u20131135, Theorem 4.1]. Second, we prove the following: Let [Formula: see text] be a [Formula: see text]-stable group and [Formula: see text]. Suppose that [Formula: see text]. If [Formula: see text] is a strongly closed subgroup in [Formula: see text], then [Formula: see text], [Formula: see text] and [Formula: see text] are normal subgroups of [Formula: see text]. Third, we show the following: Let [Formula: see text] be a [Formula: see text]-free group and [Formula: see text]. If [Formula: see text] is a strongly closed subgroup in [Formula: see text], then the normalizers of the subgroups [Formula: see text], [Formula: see text] and [Formula: see text] control strong [Formula: see text]-fusion in [Formula: see text]. We also prove a similar result for a [Formula: see text]-stable and [Formula: see text]-constrained group. Finally, we give a [Formula: see text]-nilpotency criteria, which is an extension of Glauberman\u2013Thompson [Formula: see text]-nilpotency theorem.<\/jats:p>","DOI":"10.1142\/s0218196721500065","type":"journal-article","created":{"date-parts":[[2020,9,16]],"date-time":"2020-09-16T15:03:37Z","timestamp":1600268617000},"page":"117-133","source":"Crossref","is-referenced-by-count":1,"title":["An extension of the Glauberman ZJ-theorem"],"prefix":"10.1142","volume":"31","author":[{"given":"M. Yasir","family":"K\u0131zmaz","sequence":"first","affiliation":[{"name":"Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,10,30]]},"reference":[{"key":"S0218196721500065BIB001","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511794506"},{"key":"S0218196721500065BIB002","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1968-107-2"},{"key":"S0218196721500065BIB004","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1515\/9783110198126.105","volume-title":"Finite Groups 2003","author":"Glauberman G.","year":"2004"},{"key":"S0218196721500065BIB005","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1997.7090"},{"key":"S0218196721500065BIB006","volume-title":"Finite Groups","author":"Gorenstein D.","year":"2007","edition":"2"},{"key":"S0218196721500065BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2018.11.029"},{"key":"S0218196721500065BIB008","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/092"},{"key":"S0218196721500065BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(70)90092-X"},{"key":"S0218196721500065BIB010","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.2000.8747"},{"key":"S0218196721500065BIB011","volume-title":"The Theory of Finite Groups: An Introduction","author":"Kurzweil H.","year":"2006"},{"key":"S0218196721500065BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2016.06.001"},{"key":"S0218196721500065BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(64)90006-7"},{"key":"S0218196721500065BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(69)90068-4"},{"key":"S0218196721500065BIB015","doi-asserted-by":"publisher","DOI":"10.1090\/proc\/15066"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196721500065","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,18]],"date-time":"2022-11-18T17:12:27Z","timestamp":1668791547000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196721500065"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,30]]},"references-count":14,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2021,2]]}},"alternative-id":["10.1142\/S0218196721500065"],"URL":"https:\/\/doi.org\/10.1142\/s0218196721500065","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,30]]}}}