2025/10/27 by Jaikin-Zapirain, Andrei, Linton, Marco, Sánchez-Peralta, Pablo
#20E07 #20J05 (Primary) 20E08 (Secondary) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2510.23518
A group pair (G, X) consists of a group G together with a G-set X. Such a pair encodes properties of G relative to the stabilisers of points in X. In this paper, we show how to combine properties of group pairs and their stabilisers to prove coherence results for G and its group algebra, as well as to study the quotient of G obtained by killing the stabilisers. In particular, we prove that a torsion-free one-relator product of locally indicable groups is coherent provided that both factor groups are coherent. Moreover, we show that the group algebra of such a group over a field of characteristic 0 is coherent whenever the group algebras of the factors are coherent. As other consequences of our methods, we also show that extensions of coherent locally indicable hyperbolic groups by ℤ are coherent and that groups admitting a Cohen--Lyndon presentation satisfy the Farrell--Jones Conjecture for K0.