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Turkish Journal of Mathematics

Article Title

n-Commutator Groups

DOI

-

Abstract

A sufficient condition such that any element of G' (the commutator subgroup of G) can be represented as a product of n commutators, was studied in \cite{GAL62}. In this article we study a necessary and sufficient condition such that any element of G' can be represented as a product of n commutators, Let n be the smallest nature number such that any element of finite group G can be represented as a product of n commutators. A group G with this property will be called an n -commutator group, and n will be denoted by c(G) . Then \frac{\ln( G' )}{\ln( G:Z(G) )} \leq 2c(G). In particular, if the all elements of G' can be represented as a commutator, then G' \leq G:Z(G) ^{2}.

First Page

237

Last Page

243

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Mathematics Commons

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