Large orbits in actions of nilpotent groups
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- by I. M. Isaacs PDF
- Proc. Amer. Math. Soc. 127 (1999), 45-50 Request permission
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
- Jerald S. Brodkey, A note on finite groups with an abelian Sylow group, Proc. Amer. Math. Soc. 14 (1963), 132–133. MR 142631, DOI 10.1090/S0002-9939-1963-0142631-X
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- D. S. Passman, Groups with normal solvable Hall $p^{\prime }$-subgroups, Trans. Amer. Math. Soc. 123 (1966), 99–111. MR 195947, DOI 10.1090/S0002-9947-1966-0195947-2
Additional Information
- I. M. Isaacs
- Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706
- Email: isaacs@math.wisc.edu
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 45-50
- MSC (1991): Primary 20D15
- DOI: https://doi.org/10.1090/S0002-9939-99-04584-0
- MathSciNet review: 1469413