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Groups with many permutable subgroups
Published online by Cambridge University Press: 09 April 2009
Abstract
We consider the influence on a group G of the condition that every infinite set of cyclic subgroups of G contains a pair that permute and prove (Theorem 1) that finitely generated soluble groups with this condition are centre-by-finite, and (Theorem 2) that torsion free groups satisfying the condition are abelian.
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- Copyright © Australian Mathematical Society 1990
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