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

James Howie, Ihechukwu Chinyere

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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.
Original languageEnglish
Pages (from-to)533-550
Number of pages18
JournalInternational Journal of Algebra and Computation
Issue number3
Publication statusPublished - May 2016


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