We state a sufficient condition for a fusion system to be saturated. This is then used to investigate localities with kernels: that is, localities that are (in a particular way) extensions of groups by localities. As an application of these results, we define and study certain products in fusion systems and localities, thus giving a new method to construct saturated subsystems of fusion systems.
Grazian, V., Henke, E. (2022). Kernels of localities. FORUM OF MATHEMATICS. SIGMA, 10(2022) [10.1017/fms.2022.59].
Kernels of localities
Grazian, V;
2022
Abstract
We state a sufficient condition for a fusion system to be saturated. This is then used to investigate localities with kernels: that is, localities that are (in a particular way) extensions of groups by localities. As an application of these results, we define and study certain products in fusion systems and localities, thus giving a new method to construct saturated subsystems of fusion systems.
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