ALGORITHMIC PROBLEMS

See also problems (O4), (05), (O8), (F1),  (F6), (OR4), (FP1), (H2), (H3), (M1), (S2), (S5), (S6).

(A1) Are there finitely generated 2-relator groups with unsolvable word problem?

(A2) (D.Collins) Can every torsion-free group with solvable word problem be embedded in a group with solvable conjugacy problem?

(A3) Let G be a finitely presented group, H the intersection of all normal subgroups of finite index in G. Can G/H have unsolvable word problem?

(A4) (L.P.Neuwirth) Is there an (algebraic) algorithm to decide if a knot group is cyclic?   Background

(A5) (V.Shpilrain) Is the set of finitely presented metabelian groups recursively enumerable? Background

(A6) (M. Chiodo) Is there a general procedure to produce a non-trivial element from a finite presentation of a non-trivial group? Background