Square-free class sizes in products of groups

Published 24 Mar 2017 in math.GR | (1703.08363v1)

Abstract: We obtain some structural properties of a factorised group $G = AB$, given that the conjugacy class sizes of certain elements in $A\cup B$ are not divisible by $p^2$, for some prime $p$. The case when $G = AB$ is a mutually permutable product is especially considered.

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