All geometries of the Mathieu group based on maximal subgroups.
Buekenhout, Francis, Dehon, Michel, Leemans, Dimitri (1996)
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Buekenhout, Francis, Dehon, Michel, Leemans, Dimitri (1996)
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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 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.
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We describe finite groups which contain just one conjugate class of self-normalizing subgroups.
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