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)

 

Large orbits in actions of nilpotent groups


Author: I. M. Isaacs
Journal: Proc. Amer. Math. Soc. 127 (1999), 45-50
MSC (1991): Primary 20D15
MathSciNet review: 1469413
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If a nontrivial nilpotent group $N$ acts faithfully and coprimely on a group $H$, it is shown that some element of $H$ has a small centralizer in $N$ and hence lies in a large orbit. Specifically, there exists $x \in H$ such that $|\mathbf{C}_{N}(x)| \le (|N|/p)^{1/p}$, where $p$ is the smallest prime divisor of $|N|$.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 20D15

Retrieve articles in all journals with MSC (1991): 20D15


Additional Information

I. M. Isaacs
Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706
Email: isaacs@math.wisc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04584-0
PII: S 0002-9939(99)04584-0
Received by editor(s): May 12, 1997
Additional Notes: This research was partially supported by a grant from the National Security Agency
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1999 American Mathematical Society