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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
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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?)

  • 1. J. S. Brodkey, A note on finite groups with an abelian Sylow group, Proc. Amer. Math. Soc. 14 (1963), 132-133. MR 26:200
  • 2. B. Hartley and A. Turull, On characters of coprime operator groups and the Glauberman character correspondence, J. Reine Angew. Math. 451 (1994), 175-219. MR 95d:20010
  • 3. D. S. Passman, Groups with normal solvable Hall $p'$-subgroups, Trans. Amer. Math. Soc. 123 (1966), 99-111. MR 33:4143

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Additional Information

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

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

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