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

James Howie; Ihechukwu Chinyere

doi:10.1142/S0218196716500223

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

James Howie, Ihechukwu Chinyere

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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.

Original language	English
Pages (from-to)	533-550
Number of pages	18
Journal	International Journal of Algebra and Computation
Volume	26
Issue number	3
DOIs	https://doi.org/10.1142/S0218196716500223
Publication status	Published - May 2016

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Electronic version of an article published as International Journal of Algebra and Computation, vol. 26, 2016, 533-550 [10.1142/S0218196716500223] ©World Scientific Publishing Company [http://www.worldscientific.com/worldscinet/ijac]
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Non-triviality of some one-relator products of three groups

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