Groups with finitely many conjugacy classes of non-normal subgroups of infinite rank

Maria De Falco; Francesco de Giovanni; Carmela Musella

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Locally soluble groups with all nontrivial normal subgroups isomorphic.

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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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Stewart E. Stonehewer (1980)

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The structure of (generalized) soluble groups for which the set of all subnormal non-normal subgroups satisfies the maximal condition is described, taking as a model the known theory of groups in which normality is a transitive relation.