| Co-Investigator(Kenkyū-buntansha) |
KIYOTA Masao Tokyo Medical and Dental University, Professor, 教養部, 教授 (50214911)
UNO Katsuhiro Osaka University, Graduate School of Science, A. Professor, 大学院・理学研究科, 助教授 (70176717)
HORIE Mitsuko Ochanomizu University, Faculty of Science, Assistant, 理学部, 助手 (70242336)
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| Research Abstract |
Let G be a finite group and BィイD2oィエD2 (G) be the principal 3-block of G (over a complete valuation ring). We proved the follwing theorem ( , were Morita equivalence means having the same module category).
Theorem.
(1) If q ≡ 2, 5 (mod 9), then the (groups PGU(3,qィイD12ィエD1) have the same Brauer category and BィイD20ィエD2 (PGU(3,qィイD12ィエD1)) and BィイD20ィエD2(PGU(3,2ィイD12ィエD1)) are Morita equivalent.
(2) If q ≡ 4, 7 (mod 9), then the (groups PGL(3,q) have the same Brauer category and BィイD20ィエD2 (PGL(3,q) and BィイD20ィエD2(PGL(3,4) are Morita equivalent.
(3) If q ≡ 2, 5 (mod 9), then the (groups SU(3,qィイD12ィエD1) have the same Brauer category and BィイD20ィエD2 (SU(3,qィイD12ィエD1)) and BィイD20ィエD2(SU(3,2ィイD12ィエD1)) are Morita equivalent.
(4) If q ≡ 4, 7 (mod 9), then the (groups SL(3,q) have the same Brauer category and BィイD20ィエD2 (SL(3,q)) and BィイD20ィエD2(SL(3,2) are Morita equivalent.
(5) If q ≡ 2, 5 (mod 9), then the (groups GU(3,qィイD12ィエD1) have the same Brauer category and BィイD20ィエD2 (GU(3,qィイD12ィエD1)) and BィイD20ィエD2(GU(3,2ィイD12ィエD1)) are Morita equivalent.
(6) If q ≡ 4, 7 (mod 9), then the (groups GL(3,q) have the same Brauer category and BィイD20ィエD2 (GL(3,q) and BィイD20ィエD2(GL(3,4) are Morita equivalent.
(7) If q ≡ 2, 5 (mod 9), then the (groups GィイD12ィエD1(q) have the same Brauer category and BィイD20ィエD2 (GィイD12ィエD1)(q) and BィイD20ィエD2(GィイD12ィエD1)(2)) are Morita equivalent.
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