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International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 9, Pages 1365-1379

Character theory of infinite wreath products

Department of Mathematics, Drexel University, Philadelphia 19104, PA, USA

Received 31 August 2003; Revised 19 March 2005

Copyright © 2005 Robert Boyer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The representation theory of infinite wreath product groups is developed by means of the relationship between their group algebras and conjugacy classes with those of the infinite symmetric group. Further, since these groups are inductive limits of finite groups, their finite characters can be classified as limits of normalized irreducible characters of prelimit finite groups. This identification is called the “asymptotic character formula.” The K0-invariant of the group C-algebra is also determined.