- Abstract:
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Let {\bf a}, {\bf b} be two recursively enumerable Turing degrees with ${\bf a}\leq_T{\bf b}$. It was shown by Bokut' [`Degrees of unsolvability of the conjugacy problem for finitely presented groups' (in Russian), {\it Algebra i Logika Sem.}, 7 (1968), no.~5, 4--70; no.~6, 4--52] and Collins [`Recursively enumerable degrees and the conjugacy problem', {\it Acta. Math.}, 122 (1969), 115--160] that there are finitely presented groups with solvable word problem but with conjugacy problem of degree {\bf b}. Later on Collins [`Representation of Turing reducibility by word and conjugacy problems in finitely presented groups', {\it Acta. Math.}, 128 (1972), 73--90] generalised this by showing that there are finitely presented groups with word problem of degree {\bf a} and conjugacy problem of degree {\bf b}.
In this paper we provide new proofs of these results. The proofs use modular machines and certain normal forms for Britton towers which were introduced by Bokut' [`On a property of the Boone groups' (in Russian), {\it Algebra i Logika Sem.}, 5 (1966) No. 5, 5--23; 6 (1967) No.1, 15--24]. A fair amount of simplification results from this approach.
- Links To Paper
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- Bibtex format
- @Article{EDI-INF-RR-0894,
- author = {
Kyriakos Kalorkoti
},
- title = {Turing Degrees and the Word and Conjugacy Problems for Finitely Presented Groups},
- journal = {South East Asian Bulletin of Mathematics},
- year = 2006,
- month = {Dec},
- volume = {30},
- pages = {855-888},
- }
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