Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type.
Broto, Carles.
Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type. - 1st ed. - 1 online resource (176 pages) - Memoirs of the American Mathematical Society Series ; v.262 . - Memoirs of the American Mathematical Society Series .
Cover -- Title page -- Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type by Carles Broto, Jesper M. Møller, and Bob Oliver -- Introduction -- Tables of substitutions for Theorem B -- Chapter 1. Tame and reduced fusion systems -- Chapter 2. Background on finite groups of Lie type -- Chapter 3. Automorphisms of groups of Lie type -- Chapter 4. The equicharacteristic case -- Chapter 5. The cross characteristic case: I -- Chapter 6. The cross characteristic case: II -- Appendix A. Injectivity of _ by Bob Oliver -- A.1. Classical groups of Lie type in odd characteristic -- A.2. Exceptional groups of Lie type in odd characteristic -- Bibliography for Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type -- Automorphisms of Fusion Systems of Sporadic Simple Groups by Bob Oliver -- Introduction -- Chapter 1. Automorphism groups of fusion systems: Generalities -- Chapter 2. Automorphisms of 2-fusion systems of sporadic groups -- Chapter 3. Tameness at odd primes -- Chapter 4. Tools for comparing automorphisms of fusion and linking systems -- Chapter 5. Injectivity of _ -- Bibliography for Automorphisms of Fusion Systems of Sporadic Simple Groups -- Back Cover.
For a finite group G of Lie type and a prime p, the authors compare the automorphism groups of the fusion and linking systems of G at p with the automorphism group of G itself. When p is the defining characteristic of G, they are all isomorphic, with a very short list of exceptions. When p is different from the defining characteristic, the situation is much more complex but can always be reduced to a case where the natural map from \mathrm(G) to outer automorphisms of the fusion or linking system is split surjective. This work is motivated in part by questions involving extending the local structure of a group by a group of automorphisms, and in part by wanting to describe self homotopy equivalences of BG^\wedge _p in terms of \mathrm(G).
9781470455071
Finite simple groups.
Electronic books.
QA177 / .B768 2019
512.20000000000005
Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type. - 1st ed. - 1 online resource (176 pages) - Memoirs of the American Mathematical Society Series ; v.262 . - Memoirs of the American Mathematical Society Series .
Cover -- Title page -- Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type by Carles Broto, Jesper M. Møller, and Bob Oliver -- Introduction -- Tables of substitutions for Theorem B -- Chapter 1. Tame and reduced fusion systems -- Chapter 2. Background on finite groups of Lie type -- Chapter 3. Automorphisms of groups of Lie type -- Chapter 4. The equicharacteristic case -- Chapter 5. The cross characteristic case: I -- Chapter 6. The cross characteristic case: II -- Appendix A. Injectivity of _ by Bob Oliver -- A.1. Classical groups of Lie type in odd characteristic -- A.2. Exceptional groups of Lie type in odd characteristic -- Bibliography for Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type -- Automorphisms of Fusion Systems of Sporadic Simple Groups by Bob Oliver -- Introduction -- Chapter 1. Automorphism groups of fusion systems: Generalities -- Chapter 2. Automorphisms of 2-fusion systems of sporadic groups -- Chapter 3. Tameness at odd primes -- Chapter 4. Tools for comparing automorphisms of fusion and linking systems -- Chapter 5. Injectivity of _ -- Bibliography for Automorphisms of Fusion Systems of Sporadic Simple Groups -- Back Cover.
For a finite group G of Lie type and a prime p, the authors compare the automorphism groups of the fusion and linking systems of G at p with the automorphism group of G itself. When p is the defining characteristic of G, they are all isomorphic, with a very short list of exceptions. When p is different from the defining characteristic, the situation is much more complex but can always be reduced to a case where the natural map from \mathrm(G) to outer automorphisms of the fusion or linking system is split surjective. This work is motivated in part by questions involving extending the local structure of a group by a group of automorphisms, and in part by wanting to describe self homotopy equivalences of BG^\wedge _p in terms of \mathrm(G).
9781470455071
Finite simple groups.
Electronic books.
QA177 / .B768 2019
512.20000000000005