Residually finite algorithmically finite groups, their subgroups and direct products (original) (raw)
Abstract
We construct a finitely generated infinite recursively presented residually finite algorithmically finite group G, thus answering a question of Myasnikov and Osin. The group G here is “strongly infinite” and “strongly algorithmically finite,” which means that G contains an infinite Abelian normal subgroup and all finite Cartesian powers of G are algorithmically finite (i.e., for any n, there is no algorithm writing out infinitely many pairwise distinct elements of the group G n). We also formulate several open questions concerning this topic.
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References
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Authors and Affiliations
- Lomonosov Moscow State University, Moscow, Russia
A. A. Klyachko & A. K. Mongush
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- A. A. Klyachko
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Correspondence toA. A. Klyachko.
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Original Russian Text © A. A. Klyachko, A. K. Mongush, 2015, published in Matematicheskie Zametki, 2015, Vol. 98, No. 3, pp. 372–377.
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Klyachko, A.A., Mongush, A.K. Residually finite algorithmically finite groups, their subgroups and direct products.Math Notes 98, 414–418 (2015). https://doi.org/10.1134/S0001434615090060
- Received: 15 March 2014
- Published: 24 October 2015
- Issue Date: September 2015
- DOI: https://doi.org/10.1134/S0001434615090060