dc.contributor.author Kızmaz, M. Yasir dc.date.accessioned 2021-03-08T09:20:52Z dc.date.available 2021-03-08T09:20:52Z dc.date.issued 2020 dc.identifier.issn 0218-1967 dc.identifier.uri http://hdl.handle.net/11693/75876 dc.description.abstract Let p be an odd prime and let Jo(X), Jr(X) and Je(X) denote the three different versions of Thompson subgroups for a p-group X. In this paper, we first prove an extension of Glauberman’s replacement theorem [G. Glauberman, A characteristic subgroup of a p-stable group, Canad. J. Math. 20 (1968) 1101–1135, Theorem 4.1]. Second, we prove the following: Let G be a p-stable group and P∈Sylp(G). Suppose that CG(Op(G))≤Op(G). If D is a strongly closed subgroup in P, then Z(Jo(D)), Ω(Z(Jr(D))) and Ω(Z(Je(D))) are normal subgroups of G. Third, we show the following: Let G be a Qd(p)-free group and P∈Sylp(G). If D is a strongly closed subgroup in P, then the normalizers of the subgroups Z(Jo(D)), Ω(Z(Jr(D))) and Ω(Z(Je(D))) control strong G-fusion in P. We also prove a similar result for a p-stable and p-constrained group. Finally, we give a p-nilpotency criteria, which is an extension of Glauberman–Thompson p-nilpotency theorem. en_US dc.language.iso English en_US dc.source.title International Journal of Algebra and Computation en_US dc.relation.isversionof https://dx.doi.org/10.1142/S0218196721500065 en_US dc.subject Controlling fusion en_US dc.subject ZJ-theorem en_US dc.subject p-stable groups en_US dc.title An extension of the glauberman ZJ-theorem en_US dc.type Article en_US dc.department Department of Mathematics en_US dc.citation.spage 117 en_US dc.citation.epage 133 en_US dc.citation.volumeNumber 31 dc.citation.issueNumber 1 dc.identifier.doi 10.1142/S0218196721500065 en_US dc.publisher World Scientific en_US dc.contributor.bilkentauthor Kızmaz, M. Yasir
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