Absorption of Direct Factors With Respect to the Minimal Faithful Permutation Degree of a Finite Group

2016/10/17 by Easdown, David, Hendriksen, Michael, Saunders, Neil
#20B35 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1610.05336

Abstract

The minimal faithful permutation degree μ(G) of a finite group G is the least nonnegative integer n such that G embeds in the symmetric group \Sym(n). We prove that if H is a group then μ(G)=μ(G× H) for some group G then H embeds in A× Q^k for some abelian group of odd order, some generalised quaternion 2-group and some nonnegative integer k. As a consequence, μ(Gⁿ⁺¹)=μ(Gⁿ) for some nonnegative integer n if and only if G is trivial.

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