The rank of fusion systems

Abstract

In the early 1990s, Puig created his theory of fusion systems as a tool in modular representation theory. Later, Broto, Levi and Oliver used this theory to provide a formal setting for and prove results about the p-completed classifying spaces of finite groups. Aschbacher also started a program to establish a local theory of fusion systems similar to the local theory of finite groups. In this paper, we define the notion of ranks for fusion systems which imitates the notion of p-local ranks for finite groups and prove some results about weakly normal subsystems and factor systems.

On the local rank of fusion systems

“…By Lemma 3.1, a normal subgroup of S which is F -centric and F -radical is an m-radical subgroup in the sense of [13,Definition 3.1].…”

Statistical Analysis of the Performance of Rank Fusion Methods Applied to a Homogeneous Ensemble Feature Ranking

“…Generating a final ranking by a set of base rankings is introduced as an optimization problem known as Kemeny ranking problem [59]. In the previous literatures, some algorithms, which are collected in Figure 3, were suggested for solving this problem [19,[60][61][62][63]. ese solutions are categorized into two groups of exact and approximate solutions, although all of these algorithms are not suitable for applying in the EFR approach.…”