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The equation \([x,y]=g\) in partially commutative groups. (Russian, English) Zbl 1103.20028
Sib. Mat. Zh. 46, No. 2, 466-477 (2005); translation in Sib. Math. J. 46, No. 2, 364-372 (2005).
Summary: A partially commutative group is a group defined by generators and relations so that all defining relations are of the form: the commutators of some pairs of generators equal the identity element. We consider an algorithm for checking whether a given element of the group is a commutator, generalizing Wicks’s theorem 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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