Show simple item record

dc.contributor.authorKızmaz, M. Yasir
dc.date.accessioned2021-03-08T09:20:52Z
dc.date.available2021-03-08T09:20:52Z
dc.date.issued2020
dc.identifier.issn0218-1967
dc.identifier.urihttp://hdl.handle.net/11693/75876
dc.description.abstractLet 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.isoEnglishen_US
dc.source.titleInternational Journal of Algebra and Computationen_US
dc.relation.isversionofhttps://dx.doi.org/10.1142/S0218196721500065en_US
dc.subjectControlling fusionen_US
dc.subjectZJ-theoremen_US
dc.subjectp-stable groupsen_US
dc.titleAn extension of the glauberman ZJ-theoremen_US
dc.typeArticleen_US
dc.departmentDepartment of Mathematicsen_US
dc.citation.spage117en_US
dc.citation.epage133en_US
dc.citation.volumeNumber31
dc.citation.issueNumber1
dc.identifier.doi10.1142/S0218196721500065en_US
dc.publisherWorld Scientificen_US
dc.contributor.bilkentauthorKızmaz, M. Yasir


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record