本篇論文討論了一類非面?zhèn)鬟f的弧正則地圖。論文中將這類地圖記為M2。一般的,一個(gè)地圖M的自同構(gòu)是保持地圖各個(gè)組成部分間的關(guān)聯(lián)關(guān)系的旗集上的置換。所有這些置換在置換復(fù)合下形成M的自同構(gòu)群Aut(M)。一個(gè)地圖的重要性質(zhì)是Aut(M)總是旗集上的半正則置換群。如果Aut(M)在地圖的弧集上也是正則的,則該地圖被稱為弧正則地圖。本文的第一個(gè)重要結(jié)果是每個(gè)弧正則地圖都有一個(gè)陪集表示,即它的基本成分可以通過其自同構(gòu)群G來構(gòu)造,即地圖的點(diǎn),邊以及面可以由一些群G的子群的陪集表示。根據(jù)G的邊穩(wěn)定子的作用,弧正則地圖可以被進(jìn)一步分為兩類:面?zhèn)鬟f地圖和面不傳遞地圖。我們用M2表示第二類弧正則地圖。通過將地圖的點(diǎn),邊和面視為支撐曲面S三角剖分的0維胞腔、1維胞腔和2維胞腔,每個(gè)地圖都具有Euler示性數(shù)。本文旨在研究Euler示性數(shù)為負(fù)素?cái)?shù)的M2的分類,并通過對(duì)M2地圖的陪集表示,將對(duì)其的分類刻畫問題轉(zhuǎn)化為了對(duì)具有特定性質(zhì)群的分類問題。一個(gè)弧正則地圖的Euler示性數(shù)r對(duì)其陪集表示對(duì)應(yīng)的群G的Sylow子群有很大限制,如果r整除|G|,則G的每個(gè)Sylow p-子群包含指數(shù)為p的循環(huán)子群或二面體子群,而如果...

【文章頁數(shù)】：74 頁

【學(xué)位級(jí)別】：碩士

【文章目錄】：
ABSTRACT (In Chinese)
ABSTRACT (In English)
Chapter 1 Introduction
    1.1 Research Bacground
    1.2 Significance
    1.3 Structure and Results of This Thesis
Chapter 2 Preliminaries
    2.1 Basic Concepts
    2.2 Solvable Group
    2.3 Nilpotent
    2.4 Frattini Subgroup
    2.5 Fitting Subgroup
    2.6 Classical Group
    2.7 Extension
    2.8 Results about Dihedral Groups and p-Groups
    2.9 Basic Results in Topology Theory
    2.10 Fundamental Group
    2.11 Manifolds and Surfaces
    2.12 Maps
    2.13 Brief Summary
Chapter 3 Coset representation of arc-regular maps
    3.1 Construction of arc-regular maps by groups
    3.2 Basic properties of arc-regular maps
    3.3 Brief Summary
Chapter 4 The Euler characteristic connot divide|G|
    4.1 Arguments about the order of G
    4.2 Possible structures of G and conditions for generators
    4.3 Brief Summary
Chapter 5 The Euler characteristic is a divisor of the order of G
    5.1 Condition for 4-tuples(|G_v|,|G_f1|,|Gf2
|,(?))
    5.2 Arc-regular maps whose coset representation compatible with a 4-tuple con-taining an odd integer
    5.3 Arc-regular maps whose coset representation compatible 4-tuples containingonly even integers
    5.4 Brief Summary
CONCLUSIONS (In English)
CONCLUSIONS (In Chinese)
Magma Code for Example 4.2.1
References
Acknowledgements



本文編號(hào)：3752376

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