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Displaying similar documents to “Maximal Nonparabolic Subgroups of the Modular Group.”

Groups with nearly modular subgroup lattice

Francesco de Giovanni, Carmela Musella (2001)

Colloquium Mathematicae

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A subgroup H of a group G is nearly normal if it has finite index in its normal closure H G . A relevant theorem of B. H. Neumann states that groups in which every subgroup is nearly normal are precisely those with finite commutator subgroup. We shall say that a subgroup H of a group G is nearly modular if H has finite index in a modular element of the lattice of subgroups of G. Thus nearly modular subgroups are the natural lattice-theoretic translation of nearly normal subgroups. In this...

Pronormal and subnormal subgroups and permutability

James Beidleman, Hermann Heineken (2003)

Bollettino dell'Unione Matematica Italiana

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We describe the finite groups satisfying one of the following conditions: all maximal subgroups permute with all subnormal subgroups, (2) all maximal subgroups and all Sylow p -subgroups for p < 7 permute with all subnormal subgroups.

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.