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

The operator, $\chi $, of weak commutativity between isomorphic groups $G$and $G^{\varphi }$ was introduced by Sidki as \begin{equation*} \chi(G)=\left\langle G \cup G^{\varphi }\mid \lbrack g,g^{\varphi }]=1\,\forall\,g\in G\right\rangle \text{.} \end{equation*} It is known that the operator$\chi $ preserves group properties such as finiteness, solubility and alsonilpotency for finitely generated groups. We prove that if $G$ is a locallyfinite group with $exp(G)=n$, then $\chi(G)$ is locally finite and has finite$n$-bounded exponent. Further, we examine some finiteness criteria for thesubgroup $D(G) = \langle [g_1,g_2^{\varphi}] \mid g_i \in G\rangle \leqslant\chi(G)$ in terms of the set $\{[g_1,g_2^{\varphi}] \mid g_i \in G\}$.

Finiteness conditions for the weak commutativity construction