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.
Howie, J., & Chinyere, I. (2016). Non-triviality of some one-relator products of three groups. International Journal of Algebra and Computation, 26(3), 533-550. https://doi.org/10.1142/S0218196716500223