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 first part of the paper centers in the study of embeddability betweenpartially commutative groups. In [KK], for a finite simplicial graph $\Gamma$,the authors introduce an infinite, locally infinite graph $\Gamma^e$, calledthe extension graph of $\Gamma$. They show that each finite induced subgraph$\Delta$ of $\Gamma^e$ gives rise to an embedding between the partiallycommutative groups $G(\Delta)$ and $G({\Gamma})$. Furthermore, it is proventhat in many instances the converse also holds. Our first result is thedecidability of the Extension Graph Embedding Problem: there is an algorithmthat given two finite simplicial graphs {\Delta} and {\Gamma} decides whetheror not $\Delta$ is an induced subgraph of $\Gamma^e$. As a corollary we obtainthe decidability of the Embedding Problem for 2-dimensional partiallycommutative groups. In the second part of the paper, we relate the EmbeddingProblem between partially commutative groups to the model-theoretic question ofclassification up to universal equivalence. We use our characterisation totransfer algebraic and algorithmic results on embeddability to model-theoreticones and obtain some rigidity results on the elementary theory of atomic pcgroups as well as to deduce the existence of an algorithm to decide if anarbitrary pc group is universally equivalent to a 2-dimensional one.

Embeddability and universal theory of partially commutative groups