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Groups of cohomological codimension one (1908.08826v1)

Published 23 Aug 2019 in math.GR

Abstract: We show that if $H$ is an almost normal subgroup of $G$ such that both $H$ and $G$ are of type $VFP$ and vcd($G$) = vcd($H$) + 1, then $G$ is the fundamental group of a graph of groups in which all vertex and edge groups are commensurable to $H$. We also investigate almost normal subgroups of one-relator groups and duality groups.