Acta Mathematica· 2013Q1
Fusion systems and localities
- 95citations
- Q1SCImago
- 2013year
Short summary
A new class of algebraic structures, objective partial groups, is introduced, unifying existing concepts like linking systems and transporter systems, and including ordinary groups.
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduces objective partial groups, a unifying framework for various existing algebraic structures.
- Demonstrates that saturated fusion systems over finite p-groups correspond to unique centric linking systems.
- The proof utilizes the classification of finite simple groups, suggesting potential for alternative proofs.
AI-generated from the title and abstract; the full text is not read.
Abstract
We introduce objective partial groups, of which the linking systems and p-local finite groups of Broto, Levi, and Oliver, the transporter systems of Oliver and Ventura, and the F-localities of Puig are examples, as are groups in the ordinary sense. As an application we show that if F is a saturated fusion system over a finite p-group then there exists a centric linking system L having F as its fusion system, and that L is unique up to isomorphism. The proof relies on the classification of the finite simple groups in an indirect and—for that reason—perhaps ultimately removable way.
The authors' abstract, as published at the source. Acta Mathematica, 2013 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics