Displaying similar documents to “ n X -complementary generations of the Harada-Norton group H N

On groups with many nearly maximal subgroups

Silvana Franciosi, Francesco de Giovanni (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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A subgroup M of a group G is nearly maximal if the index | G : M | is infinite but every subgroup of G properly containing M has finite index, and the group G is called nearly I M if all its subgroups of infinite index are intersections of nearly maximal subgroups. It is proved that an infinite (generalized) soluble group is nearly I M if and only if it is either cyclic or dihedral.

A note on supersoluble maximal subgroup and theta-pairs.

James C. Beidleman, Howard Smith (1993)

Publicacions Matemàtiques

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A θ-pair for a maximal subgroup M of a group G is a pair (A, B) of subgroups such that B is a maximal G-invariant subgroup of A with B but not A contained in M. θ-pairs are considered here in some groups having supersoluble maximal subgroups.