Coprime actions with all orbit sizes small
HTML articles powered by AMS MathViewer
- by David Gluck
- Proc. Amer. Math. Soc. 143 (2015), 2331-2337
- DOI: https://doi.org/10.1090/S0002-9939-2014-12439-7
- Published electronically: December 8, 2014
- PDF | Request permission
Abstract:
Let a $p^{\prime }$-group $G$ act faithfully on a finite $p$-group $P$. Suppose that every $G$-orbit on $P$ has size at most $p-1$. We show that $G$ must have a regular orbit on $P$.References
- J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, $\Bbb {ATLAS}$ of finite groups, Oxford University Press, Eynsham, 1985. Maximal subgroups and ordinary characters for simple groups; With computational assistance from J. G. Thackray. MR 827219
- J. D. Dixon and A. E. Zalesskii, Finite primitive linear groups of prime degree, J. London Math. Soc. (2) 57 (1998), no.Β 1, 126β134. MR 1624805, DOI 10.1112/S0024610798005778
- I. M. Isaacs, Upper bounds for the number of irreducible character degrees of a group, J. Algebra 403 (2014), 201β222. MR 3166072, DOI 10.1016/j.jalgebra.2013.12.030
- Olaf Manz and Thomas R. Wolf, Representations of solvable groups, London Mathematical Society Lecture Note Series, vol. 185, Cambridge University Press, Cambridge, 1993. MR 1261638, DOI 10.1017/CBO9780511525971
- G. A. Miller, H. F. Blichfeldt, and L. E. Dickson, Theory and applications of finite groups, Dover Publications, Inc., New York, 1961. MR 0123600
Bibliographic Information
- David Gluck
- Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
- Email: dgluck@math.wayne.edu
- Received by editor(s): September 15, 2013
- Received by editor(s) in revised form: January 7, 2014
- Published electronically: December 8, 2014
- Communicated by: Pham Huu Tiep
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 2331-2337
- MSC (2010): Primary 20D45; Secondary 20H30
- DOI: https://doi.org/10.1090/S0002-9939-2014-12439-7
- MathSciNet review: 3326015