English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We introduce and study Polish topologies on various spaces of countableenumerated groups, where an enumerated group is simply a group whose underlyingset is the set of natural numbers. Using elementary tools and well knownexamples from combinatorial group theory, combined with the Baire categorytheorem, we obtain a plethora of results demonstrating that several phenomenain group theory are generic. In effect, we provide a new topological frameworkfor the analysis of various well known problems in group theory. We alsoprovide a connection between genericity in these spaces, the word problem forfinitely generated groups and model-theoretic forcing. Using these connections,we investigate the natural question: when does a certain space of enumeratedgroups contain a comeager isomorphism class? We obtain a sufficient conditionthat allows us to answer the question in the negative for the space of allenumerated groups and the space of left orderable enumerated groups. Wedocument several open questions in connection with these considerations.

Generic algebraic properties in spaces of enumerated groups