Representation of an infinite group

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A homomorphism of the infinite group into the group of bijections of an (in general infinite) set. Most often one considers representations of an infinite group by automorphisms of an algebraic structure; in this case the theory of representations of infinite groups is connected with the theory of representations of the group algebras of these groups.


[1] A.A. Kirillov, "Elements of the theory of representations" , Springer (1976) (Translated from Russian)
[2] B.I. Plotkin, "Groups of automorphisms of algebraic systems" , Wolters-Noordhoff (1972)
How to Cite This Entry:
Representation of an infinite group. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.I. Shtern (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article