Overgroups of root groups in classical groups

著者

• Aschbacher, Michael

書誌事項

Overgroups of root groups in classical groups

Michael Aschbacher

（Memoirs of the American Mathematical Society, no. 1140）

American Mathematical Society, 2016

注記

Includes bibliographical references

"Volume 241, number 1140 (first of 4 numbers), May 2016"

内容説明・目次

内容説明

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.

目次

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

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BB2128916X
• ISBN:
  • 9781470418458
• LCCN: 2015045925
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: v, 184 p.
• 大きさ: 26 cm
• 分類:
  • LCC : QA174.2
  • DC23 : 512.7/4
• 件名:
  • LCSH : Group theory
  • LCSH : Algebra
  • LCSH : Geometry
• 親書誌ID:
  • BA00035927