# An extension theory for partial groups and localities

@article{Gonzalez2015AnET, title={An extension theory for partial groups and localities}, author={Alex Gonzalez}, journal={arXiv: Algebraic Topology}, year={2015} }

A partial group is a generalization of the concept of group recently introduced by A. Chermak. By considering partial groups as simplicial sets, we propose an extension theory for partial groups using the concept of (simplicial) fibre bundle. This way, the classical extension theory for groups naturally extends to an extension theory of partial groups. In particular, we show that the category of partial groups is closed by extensions. We also describe the cohomological obstructions for…

## 3 Citations

Limits and colimits of partial groups

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- 2021

The purpose of this short paper is to analyse limits and colimits in the category Part of partial groups, algebraic structures introduced by A. Chermak. The class of partial groups contains a…

Extensions of homomorphisms between localities

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We show that the automorphism group of a linking system associated to a saturated fusion system
$\mathcal {F}$
depends only on
$\mathcal {F}$
as long as the object set of the…

Path partial groups

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It is well known that not every finite group arises as the full automorphism group of some group. Here we show that the situation is dramatically different when considering the category of partial…

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