Reduced Fusion Systems Over 2-Groups of Sectional Rank at Most 4

ISBN-13: 9781470415488 / Angielski

Bob Oliver

Opis

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.

Spis treści

• 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