Coprime actions with all orbit sizes small

Gluck, David

doi:10.1090/S0002-9939-2014-12439-7

Coprime actions with all orbit sizes small
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by David Gluck PDF

Proc. Amer. Math. Soc. 143 (2015), 2331-2337 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 $P$.

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