Reduced Fusion Systems over 2-Groups of Sectional Rank at Most 4 (Memoirs of the American Mathematical Society)

Oliver, Bob

American Mathematical Society（2016/01発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 100 p.
• 言語 ENG
• 商品コード 9781470415488
• DDC分類 512.23

Full Description

The author classifies all reduced, indecomposable fusion systems over finite $2$-groups of sectional rank at most $4$. The resulting list is very similar to that by Gorenstein and Harada of all simple groups of sectional $2$-rank at most $4$. But this method of proof is very different from theirs, and is based on an analysis of the essential subgroups which can occur in the fusion systems.

Contents

Introduction
Background on fusion systems
Normal dihedral and quaternion subgroups
Essential subgroups in $2$-groups of sectional rank at most $4$
Fusion systems over $2$-groups of type $G_2(q)$
Dihedral and semidihedral wreath products
Fusion systems over extensions of $UT_3(4)$
Appendix A. Background results about groups
Appendix B. Subgroups of $2$-groups of sectional rank $4$
Appendix C. Some explicit $2$-groups of sectional rank $4$
Appendix D. Actions on $2$-groups of sectional rank at most $4$
Bibliography