2022/05/07 by Hosaka, Tetsuya
#20F55 #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2205.03531
In this paper, we study the twist-conjecture for Coxeter systems and rigidity of Coxeter systems up to finite twists. For Coxeter systems (W,R) and (W,S), under the untangle-condition for conjugate subsets, we investigate separations and type(I) and type(II) subsets of R and S and give an equivalent condition of R and S that are conjugate up to finite twists. We provide one direction of approach to solving the twist-conjecture and the isomorphism problem for Coxeter groups of finite ranks.