Common transversals for coset spaces of compact groups

Autor:	Ando, Hiroshi, Thom, Andreas
Rok vydání:	2023
Předmět:	Mathematics - Group Theory Mathematics - Logic
Druh dokumentu:	Working Paper
Popis:	Let $G$ be a Polish group and let $H \leq G$ be a compact subgroup. We prove that there exists a Borel set $T \subset G$ which is simultaneously a complete set of coset representatives of left and right cosets, provided that a certain index condition is satisfied. Moreover, we prove that this index condition holds provided that $G$ is locally compact and $G/G^\circ$ is compact or $H$ is a compact Lie group. This generalizes a result which is known for discrete groups under various finiteness assumptions, but is known to fail for general inclusions of infinite groups. As an application, we prove that Bohr closed subgroups of countable, discrete groups admit common transversals. Comment: 18 pages v2 Added references and corrected typos
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.02612 Zobrazit plný text záznamu View this record from Arxiv