The conjugacy problem and Higman embeddings

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2004Embargo end date: 01 Jan 2002 English Publisher:American Mathematical Society (AMS)Journal:Memoirs of the American Mathematical Society, volume 170, pages 0-0 (issn: 0065-9266, eissn: 1947-6221,

Copyright policy )Funded by:NSF | Asymptotic and Algorithmi...

Authors: Olshanskii, A. Yu.; Sapir, M. V.;

doi: 10.1090/memo/0804 , 10.48550/arxiv.math/0212227

arXiv: math/0212227

The conjugacy problem and Higman embeddings

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Abstract

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.

Related Organizations

Vanderbilt University
United States

Keywords

FOS: Mathematics, Mathematics - Logic, Group Theory (math.GR), Logic (math.LO), Mathematics - Group Theory

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