Automorphism invariance and identities

Details Automorphism invariance and identities Automorphism invariance and identities

2008-12-07

arxiv.org/abs/0812.1359v2

Bull. London Math. Soc. 2009 41(5):804-816

Mathematics

Group Theory

8 pages. A Russian version of this paper is at http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm V2: A re

Scientific paper

10.1112/blms/bdp056

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.

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