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2013 Fiscal Year Final Research Report

Research on p-adic properties of the numbers of permutation representations

Research Project

  • PDF
Project/Area Number 22540004
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionMuroran Institute of Technology

Principal Investigator

TAKEGAHARA Yugen  室蘭工業大学, 工学(系)研究科(研究院), 教授 (10211351)

Project Period (FY) 2010-04-01 – 2014-03-31
Keywords準同型 / 対称群 / 交代群 / 環積 / p進的性質
Research Abstract

There are three results. 1) p-adic properties of the number of homomorphisms from a finite abelian p-group to symmetric groups were obtained. In particular, the exponent of p of the decomposition of such numbers into prime factors was made clear. There are 6 different types of the results. 2) The exponent of 2 in the decomposition of one plus the number of involutions in alternating groups or wreath products of a cyclic group of order 2 by alternating groups groups into prime factors could be described as 2-adic integers. 3)p-adic properties of the number of homomorphisms from the direct product of two cyclic p-groups to wreath product of a cyclic p-group by symmetric groups were obtained. The results are closely related to that for the number of homomorphisms to symmetric groups.

  • Research Products

    (7 results)

All 2014 2013 2012 2010

All Journal Article (3 results) (of which Peer Reviewed: 3 results) Presentation (4 results)

  • [Journal Article] Induction formulae for Mackey functors with applications to representations of the twisted quantum double of a finite group2014

    • Author(s)
      Y. Takegahara
    • Journal Title

      J. Algebra

      Volume: 410 Pages: 85-147

    • DOI

      10.1016/j.jalgebra.2014.03.017

    • Peer Reviewed
  • [Journal Article] On a theorem of P. Hall2013

    • Author(s)
      T. Asai, N. Chigira, T. Niwasaki, and Y. Takegahara
    • Journal Title

      J. Group Theory

      Volume: 16 Pages: 69-80

    • Peer Reviewed
  • [Journal Article] Multiple Burnside rings and Brauer induction formulae2010

    • Author(s)
      Y. Takegahara
    • Journal Title

      J. Algebra

      Volume: 324 Pages: 1656-1686

    • DOI

      10.1016/j.jalgebra.2010.05.021

    • Peer Reviewed
  • [Presentation] 2-adic properties of the number of solutions of x^m=1 in the alternating group A_n2014

    • Author(s)
      竹ヶ原裕元
    • Organizer
      有限群とその表現,頂点作用素代数, 代数的組合わせ論の研究
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      20140303-06
  • [Presentation] The crossed and monomial Burnside rings2013

    • Author(s)
      竹ヶ原裕元
    • Organizer
      第58回代数学シンポジウム
    • Place of Presentation
      広島大学
    • Year and Date
      20130826-29
  • [Presentation] バーンサイド環の一般化とその応用有限群とその表現2012

    • Author(s)
      竹ヶ原裕元
    • Organizer
      頂点作用素代数, 組合せ論の研究
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      20120305-08
  • [Presentation] Generalizations of Burnside ring and their applications2010

    • Author(s)
      竹ヶ原裕元
    • Organizer
      頂点作用素代数・有限群・組合せ論の研究
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      20101213-17

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Published: 2015-07-16  

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