On the commutator and the center of finite groups

Marcel Herzog; Gil Kaplan; Arieh Lev

doi:10.1016/j.jalgebra.2004.03.021

On the commutator and the center of finite groups

Marcel Herzog^*, Gil Kaplan, Arieh Lev

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

For a finite group G, we study the connections between the sizes of its commutator subgroup G′ and its center Z(G). For example, we prove that if G is a solvable group such that Φ(G)=1 and G′ ≤ G ^1/3, then Z(G)≠1.

Original language	English
Pages (from-to)	494-501
Number of pages	8
Journal	Journal of Algebra
Volume	278
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2004.03.021
State	Published - 15 Aug 2004

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title = "On the commutator and the center of finite groups",

abstract = "For a finite group G, we study the connections between the sizes of its commutator subgroup G′ and its center Z(G). For example, we prove that if G is a solvable group such that Φ(G)=1 and G′ ≤ G 1/3, then Z(G)≠1.",

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On the commutator and the center of finite groups

Abstract

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