Commutators in finite p-groups with 2-generator derived subgroup

2017/09/29 by Iker de las Heras, Heras, Iker de las, Gustavo A. Fernández‐Alcober +1 · 1 citation
Mathematics · #Finite Group Theory Research #Rings, Modules, and Algebras #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.1709.10422

Abstract

Let G be a finite p-group whose derived subgroup G' can be generated by 2 elements. If G' is abelian, Guralnick proved that every element of G' is a commutator. In this paper, we prove that the condition that G' should be abelian is not needed. Even more, we prove that every element of G' is a commutator of the form [x,g] for a fixed x∈ G.

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• Commutators in finite p-groups with 3-generator derived subgroup
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• On finite groups with exactly one noncommutator
• On prime-power groups in which the derived group has two generators