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arXiv · 1804.05325

Structure of words with short 2-length in a free product of groups

Ihechukwu Chinyere
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Abstract

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.

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Ihechukwu Chinyere. 2018-04-15. Structure of words with short 2-length in a free product of groups. https://arxiv.org/abs/1804.05325

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