2018/04/15 by Chinyere, Ihechukwu
#FOS: Mathematics #Group Theory (math.GR) #Group theory and generalizations
paper · doi:10.48550/arxiv.1804.05325
Howie and Duncan observed that a word in a free product with length at least two and which is not a proper power can be decomposed as a product of two cyclic subwords each of which is uniquely positioned. Using this property, they proved various important results about one-relator product of groups. In this paper, we show that similar results hold in a more general setting where we allow elements of order two.