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

Iker de las Heras; Gustavo A. Fernández-Alcober

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

Group Theory 2018-04-10 v2

Authors: Iker de las Heras , Gustavo A. Fernández-Alcober

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 $x\in G$ .

Keywords

finite groups finite group theory additive combinatorics

Cite

@article{arxiv.1709.10422,
  title  = {Commutators in finite $p$-groups with $2$-generator derived subgroup},
  author = {Iker de las Heras and Gustavo A. Fernández-Alcober},
  journal= {arXiv preprint arXiv:1709.10422},
  year   = {2018}
}

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11 pages

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

Abstract

Keywords

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