Turkish Journal of Mathematics
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}.
Keywords
Commutator subgroup, irreducible characters.
First Page
237
Last Page
243
Recommended Citation
MEHRVARZ, A. A. and AZIZI, K. (2002) "n-Commutator Groups," Turkish Journal of Mathematics: Vol. 26: No. 2, Article 9. Available at: https://journals.tubitak.gov.tr/math/vol26/iss2/9
