2015/05/22 by Ihechukwu Chinyere, Chinyere, Ihechukwu, James Howie +1
Computer Science · Mathematics · #20F05 #20F06 #20F65 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1505.06094
openalex publication_date 2015/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study a group G which is the quotient of a free product of groups by the normal closure of a word that is contained in a in a subgroup which has the form of a generalised triangle group. We use known properties of generalised triangle groups, together with detailed analyses of pictures and of words in free monoids, to prove a number of results such as a Freiheitssatz and the existence of Mayer-Vietoris sequences for such groups under suitable hypotheses. The hypotheses are weaker than those in an earlier article of Howie and Shwartz, yielding generalisations in two directions of the results in that article.