Descriptive complexity of subsets of the space of finitely generated groups

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2022-12-01

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Benli, Mustafa Gökhan
Kaya, Burak

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© 2022 Elsevier GmbHIn this paper, we determine the descriptive complexity of subsets of the Polish space of marked groups defined by various group theoretic properties. In particular, using Grigorchuk groups, we establish that the sets of solvable groups, groups of exponential growth and groups with decidable word problem are Σ20-complete and that the sets of periodic groups and groups of intermediate growth are Π20-complete. We also provide bounds for the descriptive complexity of simplicity, amenability, residually finiteness, Hopficity and co-Hopficity. This paper is intended to serve as a compilation of results on this theme.

Subject Keywords

Borel hierarchy, Descriptive complexity, Finitely generated groups, Marked groups

URI

https://hdl.handle.net/11511/101775

Journal

Expositiones Mathematicae

DOI

https://doi.org/10.1016/j.exmath.2022.08.001

Collections

Department of Mathematics, Article

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Citation Formats

M. G. Benli and B. Kaya, “Descriptive complexity of subsets of the space of finitely generated groups,” Expositiones Mathematicae, vol. 40, no. 4, pp. 1116–1134, 2022, Accessed: 00, 2023. [Online]. Available: https://hdl.handle.net/11511/101775.