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On groups with decomposable commutator subgroups

Published online by Cambridge University Press:  18 May 2009

Robert M. Guralnick
Robert M. Guralnick
Affiliation:
Department Of Mathematics, University Of California, 405 Hilgard Avenue, Los Angeles, Ca 90024
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Let G be a group. We define λ(G) to be the smallest integer n such that every element of the commutator subgroup G′ is a product of n commutators. Ito [4] has shown that λ (An)= 1 for all n. Thompson [7] has shown that λ (SLn(q))= 1 for all n and q. In fact, there is no known simple group G such that λ(G)>1. However, there do exist such perfect groups (cf. [7]).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 19 , Issue 2 , July 1978 , pp. 159 - 162
Copyright
Copyright © Glasgow Mathematical Journal Trust 1978

References

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