Nilpotency of normal subgroups having two G-class sizes
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadata
Title
Nilpotency of normal subgroups having two G-class sizesDate
2010-12-22Publisher
American Mathematical SocietyISSN
0002-9939; 1088-6826Bibliographic citation
Proceedings of the American Mathematical Society (2011), vol. 139, no. 8, p. 2663–2669Type
info:eu-repo/semantics/articlePublisher version
http://www.ams.org/journals/proc/2011-139-08/S0002-9939-2010-10702-5/S0002-9939- ...Version
info:eu-repo/semantics/publishedVersionSubject
Abstract
Let G be a finite group. If N is a normal subgroup which has exactly two G-conjugacy class sizes, then N is nilpotent. In particular, we show that N is abelian or is the product of a p-group P by a central subgroup ... [+]
Let G be a finite group. If N is a normal subgroup which has exactly two G-conjugacy class sizes, then N is nilpotent. In particular, we show that N is abelian or is the product of a p-group P by a central subgroup of G. Furthermore, when P is not abelian, P /(Z(G) ∩ P ) has exponent p. [-]
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© American Mathematical Society
info:eu-repo/semantics/openAccess
© American Mathematical Society
info:eu-repo/semantics/openAccess
This item appears in the folowing collection(s)
- MAT_Articles [749]