Some Results on Polish Groups
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RIS BIB ENDNOTESome Results on Polish Groups
Publication date: 20.08.2020
Reports on Mathematical Logic, 2020, Number 55, pp. 61-71
https://doi.org/10.4467/20842589RM.20.003.12435Authors
Some Results on Polish Groups
We prove that no quantifier-free formula in the language of group theory can define the ℵ1-half graph in a Polish group, thus generalising some results from [6]. We then pose some questions on the space of groups of automorphisms of a given Borel complete class, and observe that this space must contain at least one uncountable group. Finally, we prove some results on the structure of the group of automorphisms of a locally finite group: firstly, we prove that it is not the case that every group of automorphisms of a graph of power λ is the group of automorphism of a locally finite group of power λ; secondly, we conjecture that the group of automorphisms of a locally finite group of power λ has a locally finite subgroup of power λ, and reduce the problem to a problem on p-groups, thus settling the conjecture in the case λ = ℵ0.
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Information: Reports on Mathematical Logic, 2020, Number 55, pp. 61-71
Article type: Original article
Department of Mathematics “Giuseppe Peano”, University of Torino, Italy
Institute of Mathematics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
Department of Mathematics, Rutgers University, New Brunswick, NJ 08854, USA
Published at: 20.08.2020
Received at: 24.09.2019
Article status: Open
Licence: CC BY-NC-ND
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English