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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.

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)
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