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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Given a permutational wreath product sequence of cyclic groups we investigateits minimal generating set, minimal generating set for its commutator and someproperties of its commutator subgroup. We strengthen the result of author\cite{SkVC, SkMal, SkAr} and construct minimal generating set for wreathproduct of finite and infinite cyclic groups and direct product of such groups.We generalize results of Meldrum about commutator subgroup of wreath product\cite{Meld} because we take in consideration as regular wreath product as wellas no regular (where active group $\mathcal{A}$ can acts not faithfully). Alsocommutator of such group and its minimal generating set. Also center of suchproducts was investigated. Also fundamental group of orbits of a Morse function$f:M\to \mathbb{R}$ defined on a Mebius band $M$ with respect to the rightaction of the group of diffeomorphisms $\mathcal{D}(M)$ is investigated by us.The paper describes precise algebraic structure of the group $\pi_1 O(f)$. Aminimal set of generators for the group of orbits of functions ${{\pi}_{1}}({{O}_{f}},f)$ arising under the action of diffeomorphisms groupstabilizing the function $f$ and stabilizing $\partial M$ is found. The theMorse function $f$ has critical sets with one saddle point. The quotient groupof restricted wreath products by its commutator was found. The generic sets ofcommutator of wreath product were investigated. Minimal generating set for thisgroup and for commutator of group are found.  This paper after previous Arxiv versions from 2019 \cite{SkArM, SkArM3} withprevious title "Minimal generating set and structure of wreath product ofgroups with non-faithful action, comutator subgroup of wreath product and thefundamental group of orbit of Morse function $\pi_1 O(f)$" was published\cite{SkRendi}.

Irreducible Bases and Subgroups of a Wreath Product in Applying to Diffeomorphism Groups acting on the M\"obius Band