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Coprime actions with all orbit sizes small


Author: David Gluck
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
Published electronically: December 8, 2014
MathSciNet review: 3326015
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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$.


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Additional Information

David Gluck
Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
Email: dgluck@math.wayne.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12439-7
Keywords: Coprime actions, orbit sizes, pseudoreflections
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
Article copyright: © Copyright 2014 American Mathematical Society