Automorphism invariance and identities
Group Theory
2010-09-01 v2 Rings and Algebras
Abstract
If an outer (multilinear) commutator identity holds in a large subgroup of a group, then it holds also in a large characteristic subgroup. Similar assertions are valid for algebras and their ideals or subspaces. Varying the meaning of the word "large", we obtain many interesting facts. These results cannot be extended to arbitrary (non-multilinear) identities. As an application, we give a sharp estimate for the `virtual derived length' of (virtually solvable)-by-(virtually solvable) groups.
Cite
@article{arxiv.0812.1359,
title = {Automorphism invariance and identities},
author = {Evgenii I. Khukhro and Anton A. Klyachko and Natalia Yu. Makarenko and Yulia B. Melnikova},
journal= {arXiv preprint arXiv:0812.1359},
year = {2010}
}
Comments
8 pages. A Russian version of this paper is at http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm V2: A reference added