# Existence, uniqueness and functoriality of the perfect locality over a Frobenius P-category

@article{Puig2012ExistenceUA, title={Existence, uniqueness and functoriality of the perfect locality over a Frobenius P-category}, author={Lluis Puig}, journal={arXiv: Group Theory}, year={2012} }

Let p be a prime, P a finite p-group and F a Frobenius P-category. The question on the existence of a suitable category Lsc extending the full subcategory of F over the set of F-selfcentralizing subgroups of P goes back to Dave Benson in 1994. In 2002 Carles Broto, Ran Levi and Bob Oliver formulate the existence and the uniqueness of the category Lsc in terms of the annulation of an obstruction 3-cohomology element and of the vanishing of a 2-cohomology group, and they state a sufficient…

## 5 Citations

Note on the universality and the functoriality of the perfect F-locality

- Mathematics
- 2016

In "Frobenius Categories versus Brauer Blocks" we have proved some universality of the so-called localizing functor associated with a Frobenius $P$-category $F$, where $P$ is a finite $p$-group, with…

A Correction to the Uniqueness of a Partial Perfect Locality over a Frobenius P-Category

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Let $p$ be a prime, $P$ a finite p-group and $\cal F$ a Frobenius $P$-category. In "Existence, uniqueness and functoriality of the perfect locality over a Frobenius $P$-category", Algebra Colloquium,…

Beyond a question of Markus Linckelmann

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- 2015

In the 2002 Durham Symposium, Markus Linckelmann [1] conjectured the existence of a regular central k*-extension of the full subcategory over the selfcentralizing Brauer pairs of the Frobenius…

A Remark on the Construction of Centric Linking Systems

- Mathematics
- 2016

We give examples to show that it is not, in general, possible to prove the existence and uniqueness of centric linking systems associated to a given fusion system inductively by adding one conjugacy…

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