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Groups with boundedly finite automorphism classes. (English) Zbl 0543.20025
If G is a group then Aut G acts on G and on the set of subgroups of G. The orbits are called automorphism classes of elements, resp. subgroups. The authors give criteria for a group G to have boundedly finite automorphism classes of elements or of subgroups. A simple proof of a theorem of R. Baer [J. Reine Angew. Math. 262/263, 93-119 (1973; Zbl 0275.20079)] is given and cohomological methods used to obtain the main results. No information is given about groups in which the automorphism classes are finite but possibly unbounded.
Reviewer: M.J.Tomkinson

MSC:
20F28 Automorphism groups of groups
20F24 FC-groups and their generalizations
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References:
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