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On groups with decomposable commutator subgroups
Published online by Cambridge University Press: 18 May 2009
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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]).
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- Copyright © Glasgow Mathematical Journal Trust 1978
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