Rigid automorphisms of linking systems
| Autor: | Glauberman, George, Lynd, Justin |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Forum of Mathematics, Sigma 9 (2021) e23 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/fms.2021.17 |
| Popis: | 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 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. Comment: 21 pages; v2: minor corrections and improvements; v3: no mathematical changes |
| Databáze: | arXiv |
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