On finite groups whose derived subgroup has bounded rank

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dc.creatorPodoski, Karoly
dc.creatorSzegedy, Balazs
dc.date2007-06-22
dc.date.accessioned2026-07-07T08:11:50Z
dc.date.available2026-07-07T08:11:50Z
dc.descriptionLet $G$ be a finite group with derived subgroup of rank $r$. We prove that $\gzz\leq |G'|^{2r}$. Motivated by the results of I. M. Isaacs in \cite{isa} we show that if $G$ is capable then $\gz\leq |G'|^{4r}$. This answers a question of L. Pyber. We prove that if $G$ is a capable $p$-group then the rank of $G/\mathbf{Z}(G)$ is bounded above in terms of the rank of $G'$.
dc.identifierhttps://arxiv.org/abs/0706.3246
dc.identifierhttp://arxiv.org/abs/0706.3246
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132251
dc.subjectGroup Theory
dc.subject20D99
dc.titleOn finite groups whose derived subgroup has bounded rank
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