On the virtual and residual properties of a generalization of Bestvina-Brady groups

2022/02/16 by Leary, Ian J, Vankov, Vladimir
#20F65 (primary) 20E26 #57M07 (secondary) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2202.08169

Abstract

Previously one of us introduced a family of groups G^M_L(S), parametrized by a finite flag complex L, a regular covering M of L, and a set S of integers. We give conjectural descriptions of when G^M_L(S) is either residually finite or virtually torsion-free. In the case that M is a finite cover and S is periodic, there is an extension with kernel G_L^M(S) and infinite cyclic quotient that is a CAT(0) cubical group. We conjecture that this group is virtually special. We relate these three conjectures to each other and prove many cases of them.

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