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On Groups of Automorphisms of Residually Finite Groups

โœ Scribed by Ulderico Dardano; Bettina Eick; Martin Menth

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
111 KB
Volume
231
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

We show that certain properties of groups of automorphisms can be read off from the actions they induce on the finite characteristic quotients of their underlying group G. In particular, we obtain criteria for groups of automorphisms of a ลฝ . residually finite and soluble minimax -by-finite group G to be nilpotent or soluble.

ลฝ . Moreover, we give explicit bounds on the class the derived length, resp. of such groups of automorphisms in terms of invariants of G. Finally, we consider similar questions when G is the free group of rank two.

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