Dade's invariant conjecture for Steinberg's triality groups 3D4 (2n) in defining characteristic

Frank Himstedt, Shih-Chang Huang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)802-827
Number of pages26
JournalJournal of Algebra
Volume316
Issue number2
DOIs
Publication statusPublished - 2007 Oct 15

Fingerprint

Invariant
Preparation
Verify

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

@article{8fd5243cf91e4c65a713757839ee8f8b,
title = "Dade's invariant conjecture for Steinberg's triality groups 3D4 (2n) in defining characteristic",
abstract = "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.",
author = "Frank Himstedt and Shih-Chang Huang",
year = "2007",
month = "10",
day = "15",
doi = "10.1016/j.jalgebra.2007.01.010",
language = "English",
volume = "316",
pages = "802--827",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
number = "2",

}

Dade's invariant conjecture for Steinberg's triality groups 3D4 (2n) in defining characteristic. / Himstedt, Frank; Huang, Shih-Chang.

In: Journal of Algebra, Vol. 316, No. 2, 15.10.2007, p. 802-827.

Research output: Contribution to journalArticle

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.

UR - http://www.scopus.com/inward/record.url?scp=34548696394&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548696394&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2007.01.010

DO - 10.1016/j.jalgebra.2007.01.010

M3 - Article

VL - 316

SP - 802

EP - 827

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 2

ER -