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研究生: 陳建融
Chen, Jian-Rong
論文名稱: 8階辛群的冪單根式上Higman-Lehrer-Isaac猜想的類比
an analogue of Higman-Lehrer-Isaacs conjecture for unipotent radical of Sp8
指導教授: 粘珠鳳
Nien, Chu-feng
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系應用數學碩博士班
Department of Mathematics
論文出版年: 2014
畢業學年度: 102
語文別: 英文
論文頁數: 29
中文關鍵詞: Higman猜想Lehrer猜想Isaacs猜想q次方階次群典範子群
外文關鍵詞: Higman conjecture, Lehrer conjecture, Isaacs conjecture, q-power degree groups, pattern subgroups
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  • 這篇論文證明了一個8階辛群的冪單根式上Higman-Lehrer-Isaacs猜想的弱類比,
    其中q是一個奇質數的次方。更詳細的說,8階辛群的冪單根式的階次為q^e的不可
    分解的特徵質的個數是一個係數為非負整數的q-1的多項式。

    This thesis prove an weak analogue of Higman-Lehrer-Isaacs conjecture for the
    unipotent radical of Sp8(q), where q is a power of an odd prime. More precisely,
    the number of irreducible character of degree q^e of Sp8(q) ∩ U8 is a polynomial in
    q-1 with non-negative integer coefficients.

    1. INTRODUCTION 7 2. U4 and its pattern subgroups 9 3. Main Theorem 16 References 29

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