Geodesic
The conjugacy problem for groups, and Higman embeddings
Ol’shanskii, A.1 ; Sapir, M.2
1 Mathematics Department, Vanderbilt University, Nashville, Tennessee 37240, and Mechanics-Mathematics Department, Chair of Higher Algebra, Moscow State University, Moscow, Russia
2 Mathematics Department, Vanderbilt University, Nashville, Tennessee 37240
Electronic research announcements of the American Mathematical Society, Tome 09 (2003), pp. 40-50 Cet article a éte moissonné depuis la source American Mathematical Society

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For every finitely generated recursively presented group ${\mathcal G}$ we construct a finitely presented group ${\mathcal H}$ containing ${\mathcal G}$ such that ${\mathcal G}$ is (Frattini) embedded into ${\mathcal H}$ and the group ${\mathcal H}$ has solvable conjugacy problem if and only if ${\mathcal G}$ has solvable conjugacy problem. Moreover, ${\mathcal G}$ and ${\mathcal H}$ have the same r.e. Turing degrees of the conjugacy problem. This solves a problem by D. Collins.
DOI : 10.1090/S1079-6762-03-00110-0

Ol’shanskii, A. 1 ; Sapir, M. 2

1 Mathematics Department, Vanderbilt University, Nashville, Tennessee 37240, and Mechanics-Mathematics Department, Chair of Higher Algebra, Moscow State University, Moscow, Russia
2 Mathematics Department, Vanderbilt University, Nashville, Tennessee 37240 
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Ol’shanskii, A.; Sapir, M. The conjugacy problem for groups, and Higman embeddings. Electronic research announcements of the American Mathematical Society, Tome 09 (2003), pp. 40-50. doi: 10.1090/S1079-6762-03-00110-0

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