• Corpus ID: 247155198

A further generalization of the Glauberman-Thompson $p$-nilpotency criterion in fusion systems

  title={A further generalization of the Glauberman-Thompson \$p\$-nilpotency criterion in fusion systems},
  author={Zhencai Shen and Baoyu Zhang},
Let p be a prime and F be a saturated fusion system over a finite p-group P . The fusion system F is said to be nilpotent if F = FP (P ). We provide new criteria for a saturated fusion system F to be nilpotent, which may be viewed as extending the Glauberman-Thompson p-nilpotency criterion to fusion systems. 



Linckelmann, ZJ-theorems for fusion

  • systems, Trans. Amer. Math. Soc
  • 2008

p-Nilpotent fusion systems

  • Zhencai Shen
  • Mathematics
    Journal of Algebra and Its Applications
  • 2018
Let [Formula: see text] be a prime and let [Formula: see text] be a saturated fusion system over a finite [Formula: see text]-group [Formula: see text]. A fusion system [Formula: see text] is said to

2-Fusion in Finite Groups

Suppose A c T c G are groups such that whenever a E A, g e G, and ag E T, then as e A. In this situation, we say that A is strongly closed in T with respect to G. We are concerned here with the case

An extension of the Glauberman ZJ-theorem

A p-nilpotency criteria is given, which is an extension of Glauberman's replacement theorem and a similar result for a p-stable and p-constrained group is proved.

Fusion Systems in Algebra and Topology

A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated

Subgroup Families Controlling p‐Local Finite Groups

A p‐local finite group consists of a finite p‐group S, together with a pair of categories which encode ‘conjugacy’ relations among subgroups of S, and which are modelled on the fusion in a Sylow

ZJ-theorems for fusion systems

For p an odd prime, we generalise the Glauberman-Thompson p-nilpotency theorem [5, Ch. 8, Theorem 3.1] to arbitrary fusion systems. We define a notion of Qd(p)- free fusion systems and show that if F

The homotopy theory of fusion systems

The main goal of this paper is to identify and study a certain class of spaces which in many ways behave like p-completed classifying spaces of finite groups. These spaces occur as the “classifying

Tate's and Yoshida's theorems on control of transfer for fusion systems

We prove analogues of results of Tate and Yoshida on control of transfer for fusion systems. This requires the notions of p‐group residuals and transfer maps in cohomology for fusion systems. As a