Totally nonfree actions and infinite symmetric group

TL;DR

This paper characterizes all totally nonfree actions and adjoint-invariant measures on the subgroup lattice of the infinite symmetric group, linking group actions to character theory and factor representations.

Contribution

It provides a complete description of all adjoint-invariant and TNF-measures on the subgroup lattice of the infinite symmetric group, advancing understanding of group actions and invariant measures.

Findings

Complete classification of adjoint-invariant TNF-measures on S_N

Connections established between group actions and character theory

Results contribute to the theory of group representations

Abstract

We consider the totally nonfree (TNF) action of a groups and the corresponding adjoint invariant (AD) measures on the lattices of the subgroups of the given group. The main result is the description of all adjoint-invariant and TNF-measures on the lattice of subgroups of the infinite symmetric group $S_{\Bbb N}$. The problem is closely related to the theory of characters and factor representations of groups.