Results on Dade’s Conjecture

as of March 2001

1. SPORADIC SIMPLE GROUPS

M_{11}  final Dade [D1]
M_{12} (+coverings, outerauto.)  final Dade
M_{22} (+coverings, outerauto.)  final Huang [H]
M_{23}, M_{24}  final Schwartz, An, Conder [AC]
J_{1}  final Dade [D1]
J_{2} (+coverings, outerauto.)  final Dade
J_{3} (+coverings, outerauto.)  final Kotlica [K]
McL (+coverings)  final Murray [M], Entz, Pahlings [EP]
Ru  final Dade, An, O’Brien [AO3]
He  final An [A5]
HS  final Hassan, Horváth [HH1]
Co_{2}  final An, O’Brien [AO1]
Co_{3}  final An [A6]
Suz  final Himstedt [Hi]
O′Nan  final Uno, Yoshiara [UY]
F i_{23}  final An, O’Brien [AO2]
F i_{22}  invar. An, O’Brien [AO4]
sporadic, abelian defect principal block ord. Rouquier [Rq]

2. FINITE CHEVALLEY GROUPS

GL_{n}(q)  ord., p|q  Olsson, Uno [OU1]
GU_{n}(q)  ord., p|q  Ku [Ku]
GL_{n}(q), GU_{n}(q)  invar., p ∤ q  An [A10]
Sp_{2n}(q), SO_{m}^{±}(q)  ord., p ∤ q, p, q odd An [A11]
L_{2}(q)  final  Dade [D5]
L_{3}(q)  final, p|q  Dade
L_{n}(q)  ord., p|q  Sukizaki [S]
Sz(2^{2n+1})  final  Dade [D5]
G_{2}(q)  final, p ∤ q q ≠ 3, 4 An [A1]+
2G_{2}(3^{2n+1})  final  p ≠ 3 An [A2], p = 3 Eaton [E1]
2F_{4}(2^{2n+1})  ord., p ≠ 2  An [A3]
2F_{4}(2)′ (+ outerauto.) final  An [A4]

3. SYMMETRIC AND ALTERNATING GROUPS

A_{n}, abelian defect  ord.  Fong, Harris [FH2]
S_{n}  ord.  p ≠ 2 Olsson, Uno [OU2], p = 2 An [A8]

4. GENERAL RESULTS

cyclic defect group case  final  Dade [D4] +
tame block case  invar.  Uno [U]
abel. defect unipotent blocks  ord.  Broué, Malle, Michel [BMM]
abel. defect principal blocks  ord., p = 2 Fong, Harris [FH1]
abel. defect, some cases  ord.  Puig, Usami [PUn] [Usn]
p-solvable  proj.  Robinson [Rb1]
O_{p}(G) cyclic, G/O_{p}(G) T.I.p-Sylow proj.  Eaton [E2]

References

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