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Induced modules over group algebras and induced characters of finite groups

Research Project

Project/Area Number 13640008
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionChiba University

Principal Investigator

YAMAUCHI Kenichi  Chiba University, Faculty of Education, Professor, 教育学部, 教授 (20009690)

Co-Investigator(Kenkyū-buntansha) KITAZUME Masaaki  Chiba University, Faculty of Science, Professor, 理学部, 教授 (60204898)
KITAZUME Shigeo  Chiba University, Faculty of Science, Professor, 理学部, 教授 (30125926)
NOZAWA Sohei  Chiba University, Faculty of Science, Professor, 理学部, 教授 (20092083)
MARUYAMA Ken-ichi  Chiba University, Faculty of Education, Associate Professor, 教育学部, 助教授 (70173961)
KOSHIKAWA Hiroaki  Chiba University, Faculty of Education, Professor, 教育学部, 教授 (60000866)
Project Period (FY) 2001 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2001: ¥1,300,000 (Direct Cost: ¥1,300,000)
Keywordsfinite group / group algebra / irreducible character / representations of finite groups / induced modules / character ring / modular representations of finite groups / induced characters
Research Abstract

The objective of this research project is to study the induced modules over group algebras and the induced characters of finite groups. In the following we summarize our results.
First we proved that the Jacobson radical of the character ring of a finite group is zero, by making use of a theorem of B.Banaschewski. (B.Banaschewski, On the character rings of finite groups, Canad.J.Math. 15 (1963), 605-612.) We wrote a paper on this result.(K.Yamauchi, The bulletin of the faculty of education, Chiba Univ. Vol.51 (2003),315-317.)
Secondly we concretely constructed the units of infinite order in the character ring of a cyclic group of order p, by making use of units in Z[ω] where Z is the ring of rational integers and ω is a primitive p-th root of unity and p(【greater than or equal】 5) is a prime number, and we also proved that R(G) has units of infinite order, if the order of G/G' is divisible by a prime number p(【greater than or equal】5) where R(G) is the character ring of a finite group G and G' is the commutator subgroup of a finite group G. We wrote a paper on these results which is submitted for publication.
Finally we considered to what extent the existence of an isomorphism of R(G) onto R(H) for two finite groups G and H, can influence the modular representations of G and H. We wrote a paper on this theme which will be submitted for publication elsewhere.
Other co-workers also have made contribution to this research project and obtained excellent results on their field as well.

Report

(4 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • Research Products

    (40 results)

All Other

All Publications (40 results)

  • [Publications] 山内 憲一: "On isomorphisms of a Brauer character ring onto another, II"Journal of Algebra. 241. 808-817 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 山内 憲一: "On the Jacobson radical of the character ring of a finite group"The Bulletin of the Faculty of Education, Chiba University. 51. 315-317 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 越谷 重夫: "Conjectures of Donovan and Puig for principal 3-blocks with abelian defect groups"Communications in Algebra. 31 No.5. 2229-2243 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 越谷 重夫(共著): "Blocks of central p-group extensions"Proceedings of the American Mathematical Society. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 北詰 正顕(共著): "3-state Potts model, Moonshine vertex operator algebra and 3A-elements of the Monster group"International Mathematical Research Notices. 23. 1269-1303 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 丸山 研一: "π_* -kernels of Lie groups"Transactions of the American Mathematical Society. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kenichi Yamauchi: "On isomorphisms of a Brauer character ring onto another, II"Journal of Algebra. 241. 808-817 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kenichi Yamauchi: "On the Jacobson radical of the character ring of a finite group"The Bulletin of the Faculty of Education, Chiba University. 51. 315-317 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Shigeo Koshitani (with G.O.Michler): "Glauberman correspondence of p-blocks of finite groups"Journal of Algebra. 243. 504-517 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Shigeo Koshitani (with N.Kunugi): "The principal 3-blocks of the 3-dimensional projective special unitary groups in non-defining characteristic"Journal fuer die reine und angewandte Mathematik. 539. 1-27 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Shigeo Koshitani (with H.Miyachi): "Donovan conjecture and Loewy length for principal 3-blocks of finite groups with elementary abelian Sylow 3-group of order 9"Communications in Algebra. 29. 4509-4522 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Shigeo Koshitani (with N.Kunugi, K.Waki): "Broue's conjecture holds for principal 3-blocks with elementary abelian defect group of order 9"Journal of Algebra. 248. 575-604 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Shigeo Koshitani (with N.Kunugi, K.Waki): "Broue's conjecture for non-principal 3-blocks of finite groups"Journal of Pure and Applied Algebra. 173. 177-211 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Masaaki Kitazume (with C.H.Lam, H.Yamada): "A class of vertex operator algebras constructed from Z_8 codes"Journal of Algebras. 242. 338-359 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Masaaki Kitazume (with M.Miyamoto): "3-transposition automorphism groups of VOA, in "Finite Groups Theory and Combinatorics in honor of Michio Suzuki""Advanced Studies in Pure Mathematics. 32. 315-324 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Masaaki Kitazume (with A.Munemasa): "Even Unimodular Gaussian Lattices of Rank 12"Journal of Number Theory. 95. 77-94 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Masaaki Kitazume (with M.Harada): "Z_6-Code Constructions of the Leech Lattice and the Niemeier Lattices"European Journal of Combinatorics. 23. 573-581 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Masaaki Kitazume (with C.H.Lam, H.Yamada): "Moonshine Vertex Operator Algebra as L(1/2, 0)【cross product】L(7/10, 0)【cross product】L(4/5,0)【cross product】L(1,0)-modules"Journal of Pure and Applied Algebra. 173. 15-48 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Masaaki Kitazume (with S.Yoshiara): "The radical subgroups of the Fischer simple groups"Journal of Algebra. 255. 22-58 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Ken-ichi Maruyama: "A subgroup of self homotopy equivalences which is invariant on genus, Groups of homotopy self-equivalences and related topics"Contemporary Mathematics. 274. 225-231 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Ken-ichi Maruyama (with M.Arkowitz, D.Stanley): "The semigroup of self-homotopy classes which induce zero on homotopy groups"Kyushu Journal of Mathematics. 56. 89-107 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Ken-ichi Maruyama: "Stability properties of maps between Hopf spaces"The Quarterly Journal of Mathematics, Oxford. Second Series.. 53. 47-57 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Ken-ichi Maruyama: "π_*-kernels of Lie Groups"Transactions of the American Mathematical Society.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 越谷 重夫: "Conjectures of Donovan and Puig for principal 3-blocks with abelian defect groups"Communications in Algebra. 31 No.5. 2229-2243 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 越谷 重夫(共著): "Blocks of central p-group extensions"Proceedings of the American Mathematical Society. (発表予定).

    • Related Report
      2003 Annual Research Report
  • [Publications] 北詰 正顕(共著): "3-state Potts model, Moonshine vertex operator algebra and 3A-elements of the Monster group"International Mathematical Research Notices. 23. 1269-1303 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 越川 浩明: "Web教材についての考察"千葉大学教育学部研究紀要. 52. 307-311 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] 丸山 研一: "π_* -kernels of Lie groups"Transactions of the American Mathematical Society. (発表予定).

    • Related Report
      2003 Annual Research Report
  • [Publications] 山内憲一: "On the Jacobson radical of the character ring of a finite group"The Bulletin of The Faculty of Education, Chiba University. 51. 315-317 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] 越谷重夫 (共著): "Broue's conjecture holds for principal 3-blocks with elementary abelian defect group of order 9"Journal of Algebra. 248. 575-604 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 越谷重夫 (共著): "Broue's conjecture for non-principal 3-blocks of finite groups"Journal of Pure and Applied Algebra. 173. 177-211 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 北詰正顕 (共著): "Even Unimodular Gaussian Lattices of Rank 12"Journal of Number Theory. 95. 77-94 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 北詰正顕 (共著): "Z_6 -Code Constructions of the Leech Lattice and the Niemeier Lattices"European Journal of Combinatorics. 23. 573-581 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 丸山研一: "Stability properties of maps between Hopf spaces"The Quarterly Journal of Mathematics. 53. 47-57 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 山内 憲一: "On Isomorphisms of a Brauer Character Ring onto Another,II"Journal of Algebra. 241. 808-817 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 越谷 重夫: "Glauberman correspondence of p-blocks of finite groups"Journal of Algebra. 243. 504-517 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 越谷 重夫: "The principal 3-blocks of the 3-dimensional projective special unitary groups in non-defining characteristic"Journal fuer die reine und angewandte Mathematik. 539. 1-27 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 北詰 正顕: "A class of vertex operator algebras constructed from Zs codes"Journal of Algebra. 242. 338-359 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 北詰 正顕: "3-transposition automorphism groups of VOA in"Finite Groups Theory and Combinatorics in honor of Michio Suzuki""Advanced Studies in Pure Mathematics. 32. 315-324 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 丸山 研一: "A subgroup of self homotopy equivalences which is invariant on genus"Contemporary Mathematics. 274. 225-231 (2001)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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