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 PIPSC-type. In particular, we establish a “group-theoretic” algorithm for constructing, from a profinite group of PIPSC-type that is noncuspidal, a certain profinite graph.
"Reconstruction of profinite graphs from profinite groups of PIPSC-type." Hokkaido Math. J. 49 (3) 399 - 430, October 2020. https://doi.org/10.14492/hokmj/1607936535