Non-triviality of some one-relator products of three groups

2015/09/09 by Chinyere, Ihechukwu, Howie, James · 1 citation
#20F05 #20F06 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1509.02717

Abstract

In this paper we study a group G which is the quotient of a free product of three non-trivial groups by the normal closure of a single element. In particular we show that if the relator has length at most eight, then G is non-trivial. In the case where the factors are cyclic, we prove the stronger result that at least one of the factors embeds in G.

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