Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T19:01:12.465Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
2. Hall, P., Finiteness conditions for soluble groups, Proc. London Math. Soc. (3) 4 (1954), 419–436.Google Scholar
3. Hartley, B., The residual finiteness of wreath products, Proc. London Math. Soc. (3) 20 (1970), 365–392.Google Scholar
4. Hartley, B., On residually finite p-groups, Symposia Math. 17 (1976), 225–234.Google Scholar
5. Higman, G., Finite groups having isomorphic images in every finite group of which they are homomorphic images, Quart. J. Math., Oxford Series 6 (1955), 250–254.Google Scholar
6. Kuros, A. G., The theory of groups, Vol. II, trans. Hirsch, K. A. (Chelsea, New York, 1956).Google Scholar
7. Robinson, Derek J. S., Finiteness conditions and generalized soluble groups, Parts 1 and 2 (Springer-Verlag, Berlin, 1972).Google Scholar
8. Tits, J., Free subgroups in linear groups, J. Algebra 20 (1972), 250–270.Google Scholar