Squares of real conjugacy classes in finite groups

2024/02/09 by Beltrán, Antonio, Felipe, María José, Melchor, Carmen · 1 citation
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2402.06243

Abstract

We prove that if a finite group G contains a conjugacy class K whose square is of the form 1 ∪ D, where D is a conjugacy class of G, then ⟨ K ⟩ is a solvable proper normal subgroup of G and we completely determine its structure. We also obtain the structure of those groups in which the assumption above is true for all non-central conjugacy classes and when every conjugacy class satisfies that its square is the union of all central conjugacy classes except at most one.

Cited by

• Orders of commutators and Products of conjugacy classes in finite groups

Related

• Multiplying a conjugacy class by its inverse in a finite group
• Real class sizes
• Groups with conjugacy classes of coprime sizes
• Squares of conjugacy classes and a variant on the Baer-Suzuki Theorem
• Some problems about products of conjugacy classes in finite groups