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A Conjecture of Bachmuth and Mochizuki on Automorphisms of Soluble Groups

Published online by Cambridge University Press:  20 November 2018

Brian Hartley
Brian Hartley*
Affiliation:
University of Warwick, Coventry, England
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In [1], Bachmuth and Mochizuki conjecture, by analogy with a celebrated result of Tits on linear groups [8], that a finitely generated group of automorphisms of a finitely generated soluble group either contains a soluble subgroup of finite index (which may of course be taken to be normal) or contains a non-abelian free subgroup. They point out that their conjecture holds for nilpotent-by-abelian groups and in some other cases.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 6 , 01 December 1976 , pp. 1302 - 1310
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Bachmuth, S. and Mochizuki, H. Y., Automorphisms of solvable groups, Bull. Amer. Math. Soc. 81 (1975), 420–422.Google Scholar
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8. Tits, J., Free subgroups in linear groups, J. Algebra 20 (1972), 250–270.Google Scholar