Author | Parker, Christopher. author |
---|---|
Title | Symplectic Amalgams [electronic resource] / by Christopher Parker, Peter Rowley |
Imprint | London : Springer London : Imprint: Springer, 2002 |
Connect to | http://dx.doi.org/10.1007/978-1-4471-0165-9 |
Descript | XI, 361 p. online resource |
1 Introduction -- 1.1 Symplectic Amalgams -- 1.2 Goldchmidt G4-Amalgam Again -- 2 Preliminaries -- 2.1 Some Group Theory Results -- 2.2 Some Representation Theory Results -- 2.3 Sesquilinear Forms -- 2.4 Two Theorems of McLaughlin -- 2.5 Ultraspecial and Extraspecial Groups -- 2.6 Tensor Products and Group Actions on p-Groups -- 2.7 The Goldschmidt Amalgams -- 3 The Structure of SL2(q) and its Modules -- 3.1 Group Theoretic Properties of SL2(q) -- 3.2 Modules for SL2(q) -- 4 Elementary Properties of Symplectic Amalgams -- 4.1 The Coset Graph -- 4.2 Proof of Theorem 1.6 -- 5 The Structure of Q? -- 6 The L?-Chief Factors in V? -- 7 Reduced Symplectic Amalgams -- 7.1 A Reduced Symplectic Subamalgam -- 7.2 Reduced Amalgams and Consequences of Theorem 6.1 -- 8 The Largest Normal p?-Subgroup of L?/Q? -- 9 The Components of L?/Q? -- 9.1 The Action of L? on Compp(L?) -- 9.2 Two or more Normal Components in L?/Q? -- 10 The Reduction to Quasisimple when $$ C_{U_\alpha } (U_\alpha /Z_\alpha ) \nleqslant Q_\beta $$ -- 11 A First Look at the Amalgams with ?/Z(V?)| = q4 -- 11.1 A Characteristic 3 Amalgam -- 11.2 The Proof of Theorem 11.1 -- 12 The Story so Far -- 13 Groups of Lie Type -- 13.1 Weyl Groups and Parabolic Subgroups -- 13.2 Sylow p-subgroups of Lie Type Groups -- 13.3 Automorphisms and Centres -- 13.4 The Order of Abelian p-subgroups -- 13.5 Extremal Subgroups -- 14 Modules for Groups of Lie Type -- 14.1 Modules in Characteristic p -- 14.2 Module Results for Low Rank Groups of Lie Type -- 14.3 Modules for Lie Type Groups and (2, q)-Transvections -- 14.4 Natural Modules for Orthogonal Groups -- 14.5 Natural Modules for the Symplectic Groups -- 14.6 Natural Modules for G2(q) -- 14.7 Some Spin Modules -- 14.8 Modules for Lie Type Groups in Non-defining Characteristic -- 14.9 Some Non-containments -- 15 Sporadic Simple Groups and Their Modules -- 16 Alternating Groups and Their Modules -- 17 Rank One Groups -- 18 Lie Type Groups in Characteristic p and Rank ? -- 18.1 A Subamalgam of A -- 18.2 The Examples -- 18.3 L?/Q? a Symplectic Group and V?/Z(V?) a Spin Module -- 19 Lie Type Groups and Natural Modules -- 19.1 The Symplectic and Orthogonal Groups -- 19.2 Sp4(2) โ A Special Case -- 19.3 Groups of Type G2(q) -- 20 Lie Type Groups in Characteristic not p -- 21 Alternating Groups -- 21.1 Large Alternating Groups -- 21.2 Small Alternating Groups -- 22 Sporadic Simple Groups -- 23 The Proof of the Main Theorems -- 24 A Brief Survey of Amalgam Results -- 24.1 Amalgam Results -- 24.2 Pushing-up -- References -- Indexs