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Classification of ideals in integral group rings

Research Project

Project/Area Number 06640035
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionAichi University of Education

Principal Investigator

TAHARA Kenichi  Aichi Univ.Educ.Math.Sci.Prof., 教育学部・総合科学課程, 教授 (00024026)

Co-Investigator(Kenkyū-buntansha) 安本 太一  愛知教育大学, 教育学部, 助手 (00231647)
古川 靖邦  愛知教育大学, 教育学部, 教授 (90024033)
林 誠  愛知教育大学, 教育学部, 教授 (40109369)
Project Period (FY) 1994 – 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1996: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1995: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1994: ¥800,000 (Direct Cost: ¥800,000)
KeywordsAugmentation ideal / Dimension subgroup problem / General Fox subgroups / Generalized dimension subgroup problem / Augmentation ideal / 相対的次元部分群問題
Research Abstract

We will get a almost complete solution for long standing "dimension subgroup priblem" in integral group rings, and so we propose two methods extending the dimension subgroup problem.
1) identification of subgroups G* (1+DELTA^n (G) DELTA (H)) for any n*1
2) identification of subgroups G* (1+DELTA^n (G) +DELTA (G) DELTA (H)) for any n*1
For these problems we could identify the following subgroups
3) G* (1+DELTA^3 (G) +DELTA (G) DELTA (H))
4) G* (1+DELTA (H) DELTA (G) DELTA (H) +DELTA([H,G]) DELTA (H))
5) G* (1+DELTA^2 (G) DELTA (H) +DELTA (K) DELTA (H)) for some subgroup K determined by H.
On the other hand, when G/H is elementary abelian p-group, and any n, we could get a upper bound for the following subgroup G* (1+DELTA^n (G) DELTA (H) * U (n) V (n) H' where U (n), and V (n) are subgroups determined by H.

Report

(4 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • 1995 Annual Research Report
  • 1994 Annual Research Report
  • Research Products

    (26 results)

All Other

All Publications (26 results)

  • [Publications] K. Tahara & J. Xiao: "On the sevench dimension subgroups" Japan. J. Moth New Sor. 20. 199-212 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] K. Tahara & L. R. Vermani: "On gneralized third demension subgroubs" Canad. Math. Bull.41.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M. Hayashi & Y. Tanaka: "Qn finite simple groups all of those 2-local subgroups are solvable" J. Algebva. 191.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Y Furukawa: "Homotopy normality of hie groubs III" Hiroshima Math. J.25. 83-96 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Y Takeuchi: "Pertial solutcoic of the bad orkiefold conyeoture" Topalsgy and its Appl. 72. 113-120 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] H Uemura: "Constraction of the solution 1-dimensional heat equation with while noise potential and its asymptotic behaviour" Stock Arci Appl. 14. 487-506 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 湯浅太一,安本太一,他2名: "TOPLE : SIMD型超並列計算のための拡張Cammon Lisp" 情報処理学会論文誌. 35. 2392-2402 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 安本太一,湯浅太一,他1名: "SIMD型超並列計算機上の拡張Cammon Lisp処理等におけるゴミ集めとその評価" 情報処理学会論文誌. 35. 2369-2580 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Ken-Ichi Tahara and Jiam Xiao: "On the seventh dimension subgroups" Japan.J.Math.New Ser.20. 199-212 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Ken-Ichi Tahara, L.R.Vermani and A.Razdan: "On generalized third dimension subgroups" to appear Canad.Math.Bull.41.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Hayashi and Y.Tanaka: "On the finite simple groups all of whose 2-local subgroups are solvable" to appear J.Algebra. 191.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Y.Furukawa: "Homotopy normality of Lie Groups III" Hiroshima Math.J.25. 83-96 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Y.Takeuchi: "Partial solution of the bad orbifold conjecture" Toplogy and its Appl.72. 113-120 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] H.Uemura: "Construction of the solution of I-dimensional heat equation with white noise potential and its asympotic behavior" Stoch.Anal.Appl.14. 487-506 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Yuasa, T.Yasumoto and other two: "TUPLE : An extended common Lisp for massively pararell SIMD architectures" Trans.Inform.Proc.Sco.Japan. 35. 2392-2402 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Yasumoto, T.Yuasa and other: "Garbage collection of an extended common Lisp system for massively paralle SIMD architecture and its evaluation" Trans.Inform.Proc.Soc.Japan. 35. 2569-2580 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] K Tahara & J Xiao: "On the seventh dimension subgroups" Japan J. Math New Ser.20. 199-212 (1994)

    • Related Report
      1996 Annual Research Report
  • [Publications] K Tahara & L.R.Vermani: "On generalized third dimension subgroups" Canad.Math.Bull.

    • Related Report
      1996 Annual Research Report
  • [Publications] M Hayashi & Y.Tanaka: "On finile simple groups all of whose 2-local subgroup are solvable" J.Algebra.

    • Related Report
      1996 Annual Research Report
  • [Publications] Y.Furukawa: "Homotopy normality of his groups III" Hiroshima Math J. 25. 83-96 (1995)

    • Related Report
      1996 Annual Research Report
  • [Publications] Y Takeuchi: "Partial solution of the bad orbifold congectur" Topology and its apple. 72. 113-120 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] H Demura: "Constraction of the solution of 1-dimensional heart equation with while noise potential and its asympotic behaveois"

    • Related Report
      1996 Annual Research Report
  • [Publications] K.I Tahara & J.Xiao: "On the seventh hie dimension subgroups" Japanese Journal of Mathematics. 20. 199-212 (1994)

    • Related Report
      1995 Annual Research Report
  • [Publications] N.Gupta & K I.Tahara: "The seventh and eighth hie dimension subgroups" Journal of Pure and Applied Algebra. 88. 107-117 (1993)

    • Related Report
      1995 Annual Research Report
  • [Publications] K.I.Tahara & J.Xiao: "On the seventh hie dimension subgroups" Japanese Journal of Mathematics22GD01:20. 199-212 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] N.Gupta & K.I.Tahara: "The Seventh and eighth hie dimension subgroups" Journal of Pure and Applied Algebra. 88. 107-117 (1993)

    • Related Report
      1994 Annual Research Report

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Published: 1994-04-01   Modified: 2016-04-21  

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