Shestakov, S. L. The equation \(x^2y^2=g\) in partially commutative groups. (Russian, English) Zbl 1115.20028 Sib. Mat. Zh. 47, No. 2, 463-472 (2006); translation in Sib. Math. J. 47, No. 2, 383-390 (2006). Summary: A partially commutative group is a group defined by generators and relations so that all defining relations are of the form: the commutator of two generators is equal to the identity element. We consider an algorithm for checking whether a given group element is a product of two squares. This generalizes a result of Wicks for free groups. Cited in 7 Documents MSC: 20F05 Generators, relations, and presentations of groups 20F12 Commutator calculus 20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) Keywords:partially commutative groups; equations in groups; relations; commutators of generators; algorithms; products of squares PDFBibTeX XMLCite \textit{S. L. Shestakov}, Sib. Mat. Zh. 47, No. 2, 463--472 (2006; Zbl 1115.20028); translation in Sib. Math. J. 47, No. 2, 383--390 (2006) Full Text: EuDML EMIS