Large characteristic subgroups with modular subgroup lattice. (English) Zbl 1448.20028
Summary: 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.
MSC:
| 20E15 | Chains and lattices of subgroups, subnormal subgroups |
| 20E07 | Subgroup theorems; subgroup growth |
| 20F19 | Generalizations of solvable and nilpotent groups |
References:
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