Higher limits over the fusion orbit category

Yalcin, Ergun

doi:10.1016/j.aim.2022.108482

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2024

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Cited by 2 publications

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“…The sharpness problem has been studied from a very general point of view also by Yalçın [Yal22], who showed that sharpness for the subgroup and the normalizer decompositions are equivalent.…”

Section: Introductionmentioning

confidence: 99%

Rigid automorphisms of linking systems

Glauberman

Lynd

2021

Forum of Mathematics, Sigma

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A rigid automorphism of a linking system is an automorphism that restricts to the identity on the Sylow subgroup. A rigid inner automorphism is conjugation by an element in the center of the Sylow subgroup. At odd primes, it is known that each rigid automorphism of a centric linking system is inner. We prove that the group of rigid outer automorphisms of a linking system at the prime $2$ is elementary abelian and that it splits over the subgroup of rigid inner automorphisms. In a second result, we show that if an automorphism of a finite group G restricts to the identity on the centric linking system for G, then it is of $p'$ -order modulo the group of inner automorphisms, provided G has no nontrivial normal $p'$ -subgroups. We present two applications of this last result, one to tame fusion systems.

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Section: Introductionmentioning

confidence: 99%