WoG 2026 Talk 1.4: Muhammad Siddiq Wira Awaldy - The Congruence Subgroup Property for Finitely Gene…

Speaker: Muhammad Siddiq Wira Awaldy Institution: Institut Teknologi Bandung Title: The Congruence Subgroup Property for Finitely Generated Branch Groups Abstract: Branch group is a class of groups that act faithfully on a rooted tree which transitive at each level of the tree and satisfying certain conditions. We study the congruence subgroup property for finitely generated branch group where we compare the profinite completion of the group with the group's closure as the subgroup of the automorphism group of the rooted tree. We prove that a finitely generated branch group satisfies congruence subgroup problem (CSP) if and only if it has a just infinite profinite completion. And furthermore, we give an algebraic characterization on such class of finitely generated branch groups.