/manager/Index ${session.getAttribute("locale")} 5 Pro- <i>C</i> congruence properties for groups of rooted tree automorphisms /manager/Repository/uon:41861 C completions of the group, where C is a pseudo-variety of finite groups. A group acting on a rooted, locally finite tree has the C-congruence subgroup property (C-CSP) if its pro-C completion coincides with the completion with respect to level stabilizers. We give a sufficient condition for a weakly regular branch group to have the C-CSP. In the case where C is also closed under extensions (for instance the class of all finite p-groups for some prime p), our sufficient condition is also necessary. We apply the criterion to show that the Basilica group and the GGS-groups with constant defining vector (odd prime relatives of the Basilica group) have the p-CSP.]]> Mon 15 Aug 2022 09:07:13 AEST ]]> Multi-GGS groups have the congruence subgroup property /manager/Repository/uon:41859 3] to the family of multi-GGS groups; that is, all multi-GGS groups except the one defined by the constant vector have the congruence subgroup property. New arguments are provided to produce this more general proof.]]> Mon 15 Aug 2022 08:46:14 AEST ]]>