A note on groups of infinite rank whose proper subgroups are abelian-by-finite

Francesco de Giovanni; Federica Saccomanno

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In this paper we investigate the structure of X-groups in which every subgroup is permutable or of finite rank. We show that every subgroup of such a group is permutable.

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Let G be an infinite, locally soluble group which is isomorphic to all its nontrivial normal subgroups. If G/G' has finite p-rank for p = 0 and for all primes p, then G is cyclic.

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