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Groups whose automorphisms are almost determined by their restriction to a subgroup. (English) Zbl 0581.20042

A group is said to be torsion separable if it has a series of finite length whose factors either are periodic or have no non-trivial periodic quotients. The main result is: Theorem. Let G be a torsion separable group and let H be a Chernikov subgroup with only finitely many conjugates. Assume that \(C_{Aut G}(H)\) is countable and \(C_{Inn G}(H)\) is Chernikov. Then G is a Chernikov group and \(| G:H^ G|\) is finite.
Reviewer: D.J.S.Robinson

MSC:

20F28 Automorphism groups of groups
20E07 Subgroup theorems; subgroup growth
20E15 Chains and lattices of subgroups, subnormal subgroups
20E36 Automorphisms of infinite groups
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References:

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