Strong Tits alternative for subgroups of Coxeter groups.

Noskov, Guennadi A.; Vinberg, Èrnest B.

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We describe finite groups which contain just one conjugate class of self-normalizing subgroups.

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On Groups whose Contranormal Subgroups are Normally Complemented

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2000 Mathematics Subject Classification: 20F16, 20E15. Groups in which every contranormal subgroup is normally complemented has been considered. The description of such groups G with the condition Max-n and such groups having an abelian nilpotent residual satisfying Min-G have been obtained.

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The symmetric group of degree six can be covered by 13 and no fewer proper subgroups.

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Groups satisfying the maximal condition on subnormal non-normal subgroups

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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.