Chief factors in Polish groups

Title: Chief factors in Polish groups
Creator: Reid, Colin D.; Wesolek, Phillip R.; Le Maãtre, François
Relation: Mathematical Proceedings of the Cambridge Philosophical Society Vol. (In Press)
Publisher Link: http://dx.doi.org/10.1017/S0305004121000505
Publisher: Cambridge University Press
Resource Type: journal article
Date: 2021
Description: In finite group theory, chief factors play an important and well-understood role in the structure theory. We here develop a theory of chief factors for Polish groups. In the development of this theory, we prove a version of the Schreier refinement theorem. We also prove a trichotomy for the structure of topologically characteristically simple Polish groups. The development of the theory of chief factors requires two independently interesting lines of study. First we consider injective, continuous homomorphisms with dense normal image. We show such maps admit a canonical factorisation via a semidirect product, and as a consequence, these maps preserve topological simplicity up to abelian error. We then define two generalisations of direct products and use these to isolate a notion of semisimplicity for Polish groups. [Final citation details to be advised.]
Subject: structure theory; Schreier refinement theorem; Polish groups
Identifier: http://hdl.handle.net/1959.13/1442457
Identifier: uon:41694
Identifier: ISSN:0305-0041
Language: eng
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