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$p$-Parts of Stabilizers in Primitive Permutation Groups

David Gluck

Abstract

Let G be a primitive permutation group on a finite set Omega. Let p^2 divide |G|, for a prime p. We show that when G is solvable, there exists a subset of Omega whose stabilizer S has the property that 1<|S|_p<|G|_p. We offer a counting argument which should be helpful when G is not solvable.

$p$-Parts of Stabilizers in Primitive Permutation Groups

Abstract

Let G be a primitive permutation group on a finite set Omega. Let p^2 divide |G|, for a prime p. We show that when G is solvable, there exists a subset of Omega whose stabilizer S has the property that 1<|S|_p<|G|_p. We offer a counting argument which should be helpful when G is not solvable.
Paper Structure (17 equations)

This paper contains 17 equations.