Characteristic subgroups in locally finite groups
Copyright policy )Characteristic subgroups in locally finite groups
If a group \(G\) possesses a subgroup \(T\) of finite index, it possesses also a proper normal subgroup of finite index. The authors want instead a characteristic subgroup \(U\), they restrict themselves to locally finite groups \(G\) and subgroups \(T\) with a finite normal series with quotients that are locally nilpotent or satisfy given outer commutator laws, such that \(U\) has a normal series of the same type. They show that such a characteristic subgroup \(U\) exists, and its index in \(G\) is bounded by a function depending on the index of \(T\), the length of the series, and the weights of the outer commutator laws.
- Sobolev Institute of Mathematics Russian Federation
- University of Brasília Brazil
- University of Upper Alsace France
Automorphisms, characteristic subgroups, Algebra and Number Theory, Characteristic subgroup, Generalizations of solvable and nilpotent groups, prescribed normal series, Invariance, Chains and lattices of subgroups, subnormal subgroups, Subgroup theorems; subgroup growth, Other classes of groups defined by subgroup chains, Outer commutator law, locally finite groups, Locally finite groups, Normal subgroup, Subgroups defined by subgroup chains, locally nilpotent subgroups, subgroups of finite index, Finite-index subgroup, Derived series, central series, and generalizations for groups, Periodic groups; locally finite groups, outer commutator laws, Locally nilpotent subgroup
Automorphisms, characteristic subgroups, Algebra and Number Theory, Characteristic subgroup, Generalizations of solvable and nilpotent groups, prescribed normal series, Invariance, Chains and lattices of subgroups, subnormal subgroups, Subgroup theorems; subgroup growth, Other classes of groups defined by subgroup chains, Outer commutator law, locally finite groups, Locally finite groups, Normal subgroup, Subgroups defined by subgroup chains, locally nilpotent subgroups, subgroups of finite index, Finite-index subgroup, Derived series, central series, and generalizations for groups, Periodic groups; locally finite groups, outer commutator laws, Locally nilpotent subgroup
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