Overgroups of Root Groups in Classical Groups (Memoirs of the American Mathematical Society)

Aschbacher, Michael

American Mathematical Society（2016/05発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 184 p.
• 言語 ENG
• 商品コード 9781470418458
• DDC分類 512.74

Full Description

The author extends results of McLaughlin and Kantor on overgroups of long root subgroups and long root elements in finite classical groups. In particular he determines the maximal subgroups of this form. He also determines the maximal overgroups of short root subgroups in finite classical groups and the maximal overgroups in finite orthogonal groups of c-root subgroups.

Contents

Introduction 3-transpositions
The $(V,f)$-setup
Direct sum decompositions
Subfield structures
Modules for alternating groups
Modules with $p=2$
The orthogonal space $\mathbf{F}_2^n$
Overgroups of long root subgroups
Maximal overgroups of long root subgroups
Subgroups containing long root elements
Overgroups of short root subgroups
Short root subgroups in symplectic groups of characteristic 2
Overgroups of subgroups in $\mathbf{R}_c$ in III
Overgroups of subgroups in $\mathbf{R}_c$ in III when $q>3$
A special case for $q=3$ in III
Overgroups of subgroups in $\mathbf{R}_c$ in III when $q=3$
A result of Stellmacher More case III with $q=3$
The proof of Theorem 1
A characterization of alternating groups
Orthogonal groups with $q=2$
The proof of Theorem 2
Symplectic and unitary groups
Symplectic and unitary groups with $q$ odd
The proof of Theorem 3
Unitary groups with $q$ even
The proofs of Theorems A and B
References