Several remarks on groups of automorphisms of free groups
Yury Neretin

TL;DR
This paper explores the structure of automorphism groups of infinite free groups, showing that certain double cosets form a semigroup and analyzing their actions on product spaces of compact groups.
Contribution
It introduces a natural semigroup structure on double cosets of automorphism groups and studies their actions on $L^2$ spaces of product groups.
Findings
Double cosets form a natural semigroup structure.
Automorphism groups act on $L^2$ spaces of product groups.
Provides insights into the algebraic and analytical properties of automorphism groups.
Abstract
Let be the group of automorphisms of a free group of infinite order. Let be the stabilizer of first generators of . We show that the double cosets of with respect to admit a natural semigroup structure. For any compact group the semigroup acts in the space on the product of copies of
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