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It is known that if a group contains an abelian subgroup of finite index, then it also has an abelian characteristic subgroup of finite index. The aim of this paper is to prove that corresponding results hold when abelian subgroups are replaced either by subgroups having a modular subgroup lattice or by quasihamiltonian subgroups.
The aim of this paper is to investigate the behaviour of uncountable groups of cardinality $${\aleph}$$ ℵ in which all proper subgroups of cardinality $${\aleph}$$ ℵ have modular subgroup lattice. It is proved here that the lattice of subgroups of such a group G is modular, provided that G has no infinite simple homomorphic images of cardinality $${\aleph}$$ ℵ . A corresponding...
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