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Displaying similar documents to “The diameter of a Lascar strong type”

Groups satisfying the maximal condition on subnormal non-normal subgroups

Fausto De Mari, Francesco de Giovanni (2005)

Colloquium Mathematicae

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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.

On Groups whose Contranormal Subgroups are Normally Complemented

Kurdachenko, L. A., Subbotin, I. Ya. (2011)

Serdica Mathematical Journal

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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.

On supplements of subgroups of finite groups

Xianhua Li, A. Ballester-Bolinches (2006)

Bollettino dell'Unione Matematica Italiana

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In this paper the concept of s-pair for a subgroup of a finite group is introduced and studied. It provides a uniform way to study the influence of some families of subgroups on the structure of a finite group. A criterion for a finite group to belong to a saturated formation and necessary and sufficient conditions for solubility, supersolvability and nilpotence of a finite group are given.