Self-derived localizations of groups
Year: 2019
Type: preprint
Abstract: We introduce several classes of localizations (idempotent monads) on the category of groups and study their properties and relations. The most interesting class is the class of localizations which coincide with their zero derived functors. We call them self-derived localizations. We prove that self-derived localizations preserve the class of nilpotent groups and that for a finite $p$-group $G$ the map $G\to LG$ is an epimorphism. We also prove that Bousfield's $HR$-localization and Baumslag's $P$-localization with respect to a set of primes $P$ are self-derived.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2946420072