24 citations · 92 across the 15 of their papers we have counts for
15 papers
Realizing Finite Groups as Automizers
Sylvia Bayard, Justin Lynd
It is shown that any finite group is realizable as the automizer in a finite perfect group of an abelian subgroup whose conjugates generate . The construction uses techn…
Punctured groups for exotic fusion systems
Ellen Henke, Assaf Libman, Justin Lynd
The transporter systems of Oliver and Ventura and the localities of Chermak are classes of algebraic structures that model the -local structures of finite groups. Other than the…
Rigid automorphisms of linking systems
George Glauberman, Justin Lynd
A rigid automorphism of a linking system is an automorphism which restricts to the identity on the Sylow subgroup. A rigid inner automorphism is conjugation by an element in the ce…
Centers of Sylow Subgroups and Automorphisms
George Glauberman, Robert Guralnick, Justin Lynd +1
Suppose that p is an odd prime and G is a finite group having no normal non-trivial p'-subgroup. We show that if a is an automorphism of G of p-power order centralizing a Sylow p-g…
Weight conjectures for fusion systems
Radha Kessar, Markus Linckelmann, Justin Lynd +1
Many of the conjectures of current interest in the representation theory of finite groups in characteristic are local-to-global statements, in that they predict consequences fo…
Fusion systems with Benson-Solomon components
Ellen Henke, Justin Lynd
The Benson-Solomon systems comprise a one-parameter family of simple exotic fusion systems at the prime . The results we prove give significant additional evidence that these ar…
Weights in a Benson-Solomon block
Justin Lynd, Jason Semeraro
To each pair consisting of a saturated fusion system over a -group together with a compatible family of Külshammer-Puig cohomology classes, one can count weights in a hypothetic…
Extensions of the Benson-Solomon fusion systems
Ellen Henke, Justin Lynd
The Benson-Solomon systems comprise the only known family of simple saturated fusion systems at the prime two that do not arise as the fusion system of any finite group. We determi…
Fusion systems with some sporadic J-components
Justin Lynd, Julianne Rainbolt
Aschbacher's program for the classification of simple fusion systems of "odd" type at the prime 2 has two main stages: the classification of 2-fusion systems of subintrinsic compon…
Control of fixed points and existence and uniqueness of centric linking systems
George Glauberman, Justin Lynd
A. Chermak has recently proved that to each saturated fusion system over a finite -group, there is a unique associated centric linking system. B. Oliver extended Chermak's proof…
A characterization of the 2-fusion system of L_4(q)
Justin Lynd
We study a saturated fusion system F on a finite 2-group S having a Baumann component based on a dihedral 2-group. Assuming F is 2-perfect with no nontrivial normal 2-subgroups, an…
The Thompson-Lyons transfer lemma for fusion systems
Justin Lynd
In this note, a generalization of the Thompson transfer lemma and its various extensions, most recently due to Lyons, is proven in the context of saturated fusion systems. A streng…
Weak closure and Oliver's p-group conjecture
David J. Green, Justin Lynd
To date almost all verifications of Oliver's p-group conjecture have proceeded by verifying a stronger conjecture about weakly closed quadratic subgroups. We construct a group of o…
2-subnormal quadratic offenders and Oliver's p-group conjecture
Justin Lynd
Bob Oliver conjectures that if is an odd prime and is a finite -group, then the Oliver subgroup $\X(S)$ contains the Thompson subgroup . A positive resolution of…
Analogues of Goldschmidt's thesis for fusion systems
Justin Lynd, Sejong Park
We extend the results of David Goldschmidt's thesis concerning fusion in finite groups to saturated fusion systems and to all primes.