The conjugacy problem and Higman embeddings
نویسندگان
چکیده
منابع مشابه
The Conjugacy Problem 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. Collins.
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.
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We survey recent results about asymptotic functions of groups, obtained by the authors in collaboration with J.-C.Birget, V. Guba and E. Rips. We also discuss methods used in the proofs of these results.
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Solvability of the conjugacy problem for relatively hyperbolic groups was announced by Gromov [12]. Using the definition of Farb of a relatively hyperbolic group [9], we prove this assertion. We conclude that the conjugacy problem is solvable for the following two classes of groups: fundamental groups of complete, finite-volume, negatively curved manifolds, and finitely generated fully residual...
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The co-word problem of a group G generated by a set X is defined as the set of words in X which do not represent 1 in G. We introduce a new method to decide if a permutation group has context-free co-word problem. We use this method to show, that the Higman-Thompson groups, and therefore the Houghton groups, have context-free co-word problem. We also give some examples of groups, that even have...
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ژورنال
عنوان ژورنال: Memoirs of the American Mathematical Society
سال: 2004
ISSN: 0065-9266,1947-6221
DOI: 10.1090/memo/0804