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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We will give an example of a branch group $G$ that has exponential growth butdoes not contain any non-abelian free subgroups. This answers question 16 from\cite{Bartholdi} positively. The proof demonstrates how to construct anon-trivial word $w_{a,b}(x,y)$ for any $a,b \in G$ such that $w_{a,b}(a,b) =1$. The group $G$ is not just-infinite. We prove that every normal subgroup of$G$ is finitely generated as an abstract group and every proper quotientsoluble. Further, $G$ has infinite virtual first Betti number but is not large.

A finitely generated branch group of exponential growth without free subgroups