Cosets of normal subgroups and powers of conjugacy classes

Antonio Beltrán and María José Felipe

Mathematische Nachrichten, 2021, vol. 294, issue 9, 1652-1656

Abstract: Let G be a finite group and let K=xG be the conjugacy class of an element x of G. In this paper, it is proved that if N is a normal subgroup of G such that the coset xN is the union of K and K−1 (the conjugacy class of the inverse of x), then N and the subgroup ⟨K⟩ are solvable. As an application, we prove that if there exists a natural number n≥2 such that Kn=K∪K−1, then ⟨K⟩ is solvable.

Date: 2021
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https://doi.org/10.1002/mana.201900554

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