Author | Timmesfeld, Franz Georg. author |
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Title | Abstract Root Subgroups and Simple Groups of Lie-Type [electronic resource] / by Franz Georg Timmesfeld |
Imprint | Basel : Birkhรคuser Basel, 2001 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-7594-3 |
Descript | XIII, 389 p. online resource |
I Rank One Groups -- ยง 1 Definition, examples, basic properties -- ยง 2 On the structure of rank one groups -- ยง 3 Quadratic modules -- ยง 4 Rank one groups and buildings -- ยง 5 Structure and embeddings of special rank one groups -- II Abstract Root Subgroups -- ยง 1 Definitions and examples -- ยง 2 Basic properties of groups generated by abstract root subgroups -- ยง 3 Triangle groups -- ยง4 The radical R(G) -- ยง 5 Abstract root subgroups and Lie type groups -- III Classification Theory -- ยง 1 Abstract transvection groups -- ยง 2 The action of G on ? -- ยง 3 The linear groups and EK6 -- ยง 4 Moufang hexagons -- ยง 5 The orthogonal groups -- ยง6 D4(k) -- ยง 7 Metasymplectic spaces -- ยง8 E6(k),E7(k) and E8(k) -- ยง 9 The classification theorems -- IV Root involutions -- ยง 1 General properties of groups generated by root involutions -- ยง 2 Root subgroups -- ยง 3 The Root Structure Theorem -- ยง 4 The Rank Two Case -- V Applications -- ยง 1 Quadratic pairs -- ยง 2 Subgroups generated by root elements -- ยง3 Local BN-pairs -- References -- Symbol Index