Gilman's Conjecture
We prove a conjecture made by Gilman in 1984 that the groups presented by finite, monadic, confluent rewriting systems are precisely the free products of free and finite groups.
math.GR↗
arXiv subjects
Andy Eisenberg
Publications and source records attributed to Andy Eisenberg.
Recognizing Right-Angled Coxeter Groups Using Involutions
We consider the question of determining whether a given group (especially one generated by involutions) is a right-angled Coxeter group. We describe a group invariant, the involution graph, and we characterize the involution graphs of right-angled Coxeter groups. We use this characterization to describe a process for constructing candidate right-angled Coxeter presentations for a given group or proving that one cannot exist. We provide some first applications. In addition, we provide an elementary proof of rigidity of the defining graph for a right-angled Coxeter group. We also recover a result stating that if the defining graph contains no SILs, then Aut^0(W) is a right-angled Coxeter group.
math.GR↗
$\mathrm{CAT}(0)$ Extensions of Right-angled Coxeter Groups
We show that any split extension of a right-angled Coxeter group $W_Γ$ by a generating automorphism of finite order acts faithfully and geometrically on a $\mathrm{CAT}(0)$ metric space.
math.GR↗