M ay 2 00 4 Subgroups of finitely presented groups with solvable conjugacy problem
نویسندگان
چکیده
We prove that every countable group with solvable power problem embeds into a finitely presented 2-generated group with solvable power and conjugacy problems.
منابع مشابه
Subgroups of Finitely Presented Groups with Solvable Conjugacy Problem
We prove that every countable group with solvable power problem embeds into a finitely presented 2-generated group with solvable power and conjugacy problems.
متن کاملConjugacy in Normal Subgroups of Hyperbolic Groups
Let N be a finitely generated normal subgroup of a Gromov hyperbolic group G. We establish criteria for N to have solvable conjugacy problem and be conjugacy separable in terms of the corresponding properties of G/N . We show that the hyperbolic group from F. Haglund’s and D. Wise’s version of Rips’s construction is hereditarily conjugacy separable. We then use this construction to produce firs...
متن کاملThe Conjugacy Problem for Groups, and Higman Embeddings
For every finitely generated recursively presented group G we construct a finitely presented group H containing G such that G is (Frattini) embedded into H and the group H has solvable conjugacy problem if and only if G has solvable conjugacy problem. Moreover, G and H have the same r.e. Turing degrees of the conjugacy problem. This solves a problem by D.
متن کاملFree-by-cyclic Groups Have Solvable Conjugacy Problem
We show that the conjugacy problem is solvable in [finitely generated free]-by-cyclic groups, by using a result of O. Maslakova that one can algorithmically find generating sets for the fixed subgroups of free group automorphisms, and one of P. Brinkmann that one can determine whether two cyclic words in a free group are mapped to each other by some power of a given automorphism. We also solve ...
متن کاملFree-by-cyclic groups have solvable conjugacy problem
We show that the conjugacy problem is solvable in [finitely generated free]-by-cyclic groups, by using a result of O. Maslakova that one can algorithmically find generating sets for the fixed subgroups of free group automorphisms, and one of P. Brinkmann that one can determine whether two cyclic words in a free group are mapped to each other by some power of a given automorphism. The algorithm ...
متن کامل