Characters of Inductive Limits of Finite Alternating Groups

Invariant Random Subgroups of Inductive Limits of Finite Alternating Groups

We classify the ergodic invariant random subgroups of inductive limits of finite alternating groups.

Uniformly Recurrent Subgroups of Inductive Limits of Finite Alternating Groups

We classify the uniformly recurrent subgroups of inductive limits of finite alternating groups.

Character theory of infinite wreath products

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 identificati...

On Characters of Inductive Limits of Symmetric Groups

In the paper we completely describe characters (central positive-definite functions) of simple locally finite groups that can be represented as inductive limits of (products of) symmetric groups under block diagonal embeddings. Each such group G defines an infinite graded graph that encodes the embedding scheme. The group G acts on the space X of infinite paths of the associated graph by changi...

Finite Groups with p-Sylow Coverings