Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An analogue to Glauberman's $ ZJ$-theorem


Author: Bernd Stellmacher
Journal: Proc. Amer. Math. Soc. 109 (1990), 925-929
MSC: Primary 20D20; Secondary 20D25
Erratum: Proc. Amer. Math. Soc. 114 (1992), null.
MathSciNet review: 1013982
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ P$ be a finite $ p$-group, $ p$ an odd prime. Using certain versions of $ p$-stability it is shown that there exists a nontrivial characteristic subgroup $ W$ in $ P$ that is normal in every finite $ p$-stable group $ G$ satisfying $ {C_G}({O_p}(G)) \leq {O_p}(G)$ and $ P \in {\text{Sy}}{{\text{l}}_p}(G)$. Moreover, $ W$ contains every abelian subgroup of $ P$ normalized by $ W$.


References [Enhancements On Off] (What's this?)

  • [1] G. Glauberman, A characteristic subgroup of a $ p$-stable group, Canad. J. Math. 20 (1968), 1101-1135. MR 0230807 (37:6365)
  • [2] D. Go1dschmidt, Automorphisms of trivalent graphs, Ann. of Math. 111 (1980), 377-406. MR 569075 (82a:05052)
  • [3] D. Gorenstein, Finite groups, Harper & Row, New York. MR 0231903 (38:229)
  • [4] A. G. Kurosh, Theory of groups, Chelsea, New York, 1955.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20D20, 20D25

Retrieve articles in all journals with MSC: 20D20, 20D25


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1013982-8
PII: S 0002-9939(1990)1013982-8
Article copyright: © Copyright 1990 American Mathematical Society