TY - JOUR
T1 - Dade's invariant conjecture for Steinberg's triality groups 3D4 (2n) in defining characteristic
AU - Himstedt, Frank
AU - Huang, Shih chang
PY - 2007/10/15
Y1 - 2007/10/15
N2 - In this paper, we verify Dade's invariant conjecture for Steinberg's triality groups 3D4 (2n) in the defining characteristic, i.e., in characteristic 2. Together with the results in [J. An, Dade's conjecture for Steinberg triality groups 3D4 (q) in non-defining characteristics, Math. Z. 241 (2002) 445-469] and [J. An, F. Himstedt, S. Huang, Uno's invariant conjecture for Steinberg's triality groups in defining characteristic, in preparation], this completes the proof of Dade's conjecture for Steinberg's triality groups. Furthermore, we show that the Isaacs-Malle-Navarro version of the McKay conjecture holds for 3D4 (2n) in the defining characteristic, i.e., 3D4 (2n) is good for the prime 2 in the sense of Isaacs, Malle and Navarro.
AB - In this paper, we verify Dade's invariant conjecture for Steinberg's triality groups 3D4 (2n) in the defining characteristic, i.e., in characteristic 2. Together with the results in [J. An, Dade's conjecture for Steinberg triality groups 3D4 (q) in non-defining characteristics, Math. Z. 241 (2002) 445-469] and [J. An, F. Himstedt, S. Huang, Uno's invariant conjecture for Steinberg's triality groups in defining characteristic, in preparation], this completes the proof of Dade's conjecture for Steinberg's triality groups. Furthermore, we show that the Isaacs-Malle-Navarro version of the McKay conjecture holds for 3D4 (2n) in the defining characteristic, i.e., 3D4 (2n) is good for the prime 2 in the sense of Isaacs, Malle and Navarro.
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U2 - 10.1016/j.jalgebra.2007.01.010
DO - 10.1016/j.jalgebra.2007.01.010
M3 - Article
AN - SCOPUS:34548696394
SN - 0021-8693
VL - 316
SP - 802
EP - 827
JO - Journal of Algebra
JF - Journal of Algebra
IS - 2
ER -