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

Iker de las Heras; Gustavo A. Fernández-Alcober

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arXiv · 1709.10422

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

Iker de las Heras·Gustavo A. Fernández-Alcober

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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 $x\in G$.

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BibTeX RIS

Iker de las Heras, Gustavo A. Fernández-Alcober. 2017-09-29. Commutators in finite $p$-groups with $2$-generator derived subgroup. https://arxiv.org/abs/1709.10422

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