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|Title:||Computable torsion abelian groups||Authors:||Melnikov, Alexander G.
Ng, Keng Meng
|Keywords:||Science::Mathematics||Issue Date:||2017||Source:||Melnikov, A. G., & Ng, K. M. (2018). Computable torsion abelian groups. Advances in Mathematics, 325, 864-907. doi:10.1016/j.aim.2017.12.011||Journal:||Advances in Mathematics||Abstract:||We prove that c.c. torsion abelian groups can be described by a Π04-predicate that describes the failure of a brute-force diagonalisation attempt on such groups. We show that there is no simpler description since their index set is Π04-complete. The results can be viewed as a solution to a 60 year-old problem of Mal'cev in the case of torsion abelian groups. We prove that a computable torsion abelian group has one or infinitely many computable copies, up to computable isomorphism. The result confirms a conjecture of Goncharov from the early 1980s for the case of torsion abelian groups.||URI:||https://hdl.handle.net/10356/137680||ISSN:||0001-8708||DOI:||10.1016/j.aim.2017.12.011||Schools:||School of Physical and Mathematical Sciences||Rights:||© 2017 Elsevier Inc. All rights reserved.||Fulltext Permission:||none||Fulltext Availability:||No Fulltext|
|Appears in Collections:||SPMS Journal Articles|
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