Reconstruction of profinite graphs from profinite groups of PIPSC-type

Abstract

— In the present paper, we study profinite groups of PIPSC-type, i.e., abstract profinite groups isomorphic to the extensions determined by outer representations of PIPSCtype. In particular, we establish a “group-theoretic” algorithm for constructing, from a profinite group of PIPSC-type that is noncuspidal, a certain profinite graph.