We study automorphism groups of randomizations of separable structures, with focus on the ℵ₀-categorical case. We give a description of the automorphism group of the Borel randomization in terms of ...

Homology of the group Aut(F n ) of automorphisms of a free group on n generators is known to be independent of n in a certain stable range. Using tools from homotopy theory, we prove that in this ...

Algebraic varieties and their automorphism groups lie at the heart of modern algebraic geometry, intertwining deep theoretical concepts with practical applications. Algebraic varieties, defined as the ...

Recent advances in the study of automorphism groups within graph theory have yielded significant theoretical and applied insights. At its core, the interplay between the algebraic structure of groups ...