Large normal and characteristic subgroups satisfying outer commutator identities and their applications

Khukhro, E.I. (2008) Large normal and characteristic subgroups satisfying outer commutator identities and their applications. In: Ischia Group Theory, 1 – 4 April 2008, Naples, Italy.

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Item Type:Conference or Workshop contribution (Paper)
Item Status:Live Archive

Abstract

We discuss recent results in which a normal subgroup of finite index (or with finite rank of the quotient, or some other well-behaving parameter) satisfying an outer (multilinear) commutator law is transformed into a large characteristic subgroup satisfying the same law. Here »large» means that the index (or the corresponding parameter) of the resulting characteristic subgroup is finite and bounded in terms of the index (or the corresponding parameter) of the original normal subgroup. Similar results also hold for ideals in arbitrary algebras over a field and, moreover, for a wider class of algebraic systems defined in terms of multioperator groups. We also give examples of applications of these results in various situations involving almost soluble groups, in particular, in the study of groups with almost fixed-point-free automorphisms. © 2009 World Scientific Publishing Co. Pte. Ltd.

Additional Information:Conference Code:106075
Keywords:Algebra, Algebraic system, Automorphisms, Multi operators, Group theory
Subjects:G Mathematical and Computer Sciences > G100 Mathematics
Divisions:College of Science > School of Mathematics and Physics
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ID Code:15591
Deposited On:04 Jan 2016 14:30

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