Computing equations for residually free groups. (English) Zbl 1214.20034

Guirardel, Vincent; Levitt, Gilbert

Ill. J. Math. 54, No. 1, 129-135 (2010).

Summary: We show that there is no algorithm deciding whether the maximal residually free quotient of a given finitely presented group is finitely presentable or not.
Given a finitely generated subgroup \(G\) of a finite product of limit groups, we discuss the possibility of finding an explicit set of defining equations (i.e., of expressing \(G\) as the maximal residually free quotient of an explicit finitely presented group).

MSC:

20F10	Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
20F05	Generators, relations, and presentations of groups
20E26	Residual properties and generalizations; residually finite groups
20F65	Geometric group theory
20F67	Hyperbolic groups and nonpositively curved groups

Keywords:

algorithms; residually free quotient groups; finitely presented groups; finitely generated subgroups; finite products of limit groups

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