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A note on supersoluble maximal subgroup and theta-pairs.

James C. Beidleman, Howard Smith (1993)

Publicacions Matemàtiques

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.

Abelian groups have/are near Frattini subgroups

Simion Breaz, Grigore Călugăreanu (2002)

Commentationes Mathematicae Universitatis Carolinae

The notions of nearly-maximal and near Frattini subgroups considered by J.B. Riles in [20] and the natural related notions are characterized for abelian groups.

Intersecting maximals

A. L. Gilotti, U. Tiberio (2002)

Bollettino dell'Unione Matematica Italiana

Given a class X of finite groups and a finite group G , the authors study the subgroup X G intersection of maximal subgroups that do not belong to X .

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