Minimal fusion systems with a unique maximal parabolic

TY - JOUR

T1 - Minimal fusion systems with a unique maximal parabolic

AU - Henke, Ellen

PY - 2011/5/1

Y1 - 2011/5/1

N2 - We define minimal fusion systems in a way that every non-solvable fusion system has a section which is minimal. Minimal fusion systems can also be seen as analogs of Thompson's N-groups. In this paper, we consider a minimal fusion system F on a finite p-group S that has a unique maximal p-local subsystem containing N_F(S). For an arbitrary prime p, we determine the structure of a certain (explicitly described) p-local subsystem of F. If p=2, this leads to a complete classification of the fusion system F.

AB - We define minimal fusion systems in a way that every non-solvable fusion system has a section which is minimal. Minimal fusion systems can also be seen as analogs of Thompson's N-groups. In this paper, we consider a minimal fusion system F on a finite p-group S that has a unique maximal p-local subsystem containing N_F(S). For an arbitrary prime p, we determine the structure of a certain (explicitly described) p-local subsystem of F. If p=2, this leads to a complete classification of the fusion system F.

U2 - 10.1016/j.jalgebra.2010.11.006

DO - 10.1016/j.jalgebra.2010.11.006

M3 - Journal article

SN - 0021-8693

VL - 333

SP - 318

EP - 367

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -