# Acyclicity in finite groups and groupoids

@article{Otto2018AcyclicityIF, title={Acyclicity in finite groups and groupoids}, author={Martin Otto}, journal={ArXiv}, year={2018}, volume={abs/1806.08664} }

We expound a concise construction of finite groups and groupoids whose Cayley graphs satisfy graded acyclicity requirements. Our acyclicity criteria concern cyclic patterns formed by coset-like configurations w.r.t. subsets of the generator set rather than just by individual generators. The proposed constructions correspondingly yield finite groups and groupoids whose Cayley graphs satisfy much stronger acyclicity conditions than large girth. We thus obtain generic and canonical constructions…

## 3 Citations

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. For a ﬁnite connected graph E with set of edges E , a ﬁnite E -generated group G is constructed such that the set of relations p = 1 satisﬁed by G (with p a word over E ∪ E − 1 ) is closed under…

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Amalgamation patterns are specified by a finite collection of finite template structures together with a collection of partial isomorphisms between pairs of these. The template structures specify the…

### Comonadic semantics for guarded fragments

- Computer Science2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
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A systematic account of how a range of model comparison games which play a central role in finite model theory can be captured in terms of resource-indexed comonads on the category of relational structures, including Ehrenfeucht-Fraïssé, pebbling, and bisimulation games, is extended to quantifier-guarded fragments of first-order logic.

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