Subnormality in $P{D}_3$-groups and $L^2$-Betti numbers

Abstract

We reconsider work of Elkalla on subnormal subgroups of 3-manifold groups, giving essentially algebraic arguments that extend to the case of $P{D}_3$-groups and group pairs. However the argument relies on an $L^2$-Betti number hypothesis which has not yet been shown to hold in general.

arXiv commentThe proofs given for Lemmas 4 and 5 are irredeemably flawed.