A STUDY ON FUSION SYSTEMS OF P-GROUPS

Author (s) : J.D.Sindhanaiyarasi & DR.D.Anithadevi, DR.C.Senthilmurugan

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Abstract :
Fusion systems were introduced by L. Puig in the early 1990’s as a common framework for fusion systems of finite groups or p-blocks of finite groups. Benson suggested that every fusion system should give rise to a p-complete topological space, generalising the notion of a classifying space of a finite group. A criterion for the existence and uniqueness of such spaces was given by Broto, Levi and Oliver, who developed in the homotopy theory of a class of topological spaces, called p-local finite groups, which use fusion systems as their underlying algebraic structure. The present notes, while not touching upon the subject of p-local finite groups directly, are intended to provide a detailed introduction to fusion systems as needed in the structure theory of finite groups, p-blocks and p-local finite groups.

Keywords : Local structure of finite groups, Fusion systems, Normalisers and centralisers, Centric subgroups, Alperin’s fusion theorem, Quotients of fusion systems, Normal fusion systems, Simple fusion systems, Normal subsystems and control of fusion.

Conference Date : 17/09/2021

Pages : 264

Paper ID : IESMDT262