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)


Subgroups generated by small classes in finite groups

Author: I. M. Isaacs
Journal: Proc. Amer. Math. Soc. 136 (2008), 2299-2301
MSC (2000): Primary 20D25
Published electronically: March 14, 2008
MathSciNet review: 2390495
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ M(G)$ be the subgroup of $ G$ generated by all elements that lie in conjugacy classes of the two smallest sizes. Avinoam Mann showed that if $ G$ is nilpotent, then $ M(G)$ has nilpotence class at most $ 3$. Using a slight variation on Mann's methods, we obtain results that do not require us to assume that $ G$ is nilpotent. We show that if $ G$ is supersolvable, then $ M(G)$ is nilpotent with class at most $ 3$, and in general, the Fitting subgroup of $ M(G)$ has class at most $ 4$.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 20D25

Retrieve articles in all journals with MSC (2000): 20D25

Additional Information

I. M. Isaacs
Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706

PII: S 0002-9939(08)09263-0
Keywords: Conjugacy class size, nilpotent, supersolvable, nilpotence class
Received by editor(s): March 26, 2007
Published electronically: March 14, 2008
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2008 American Mathematical Society