本文選題：五次自由階 + 單群��； 參考：《云南財(cái)經(jīng)大學(xué)》2017年碩士論文

【摘要】：這篇論文旨在研究五次自由階擬本原置換群及其關(guān)聯(lián)的三度對稱圖(注:一個(gè)置換群G稱為d次自由階的置換群,其中d為正整數(shù),如果不存在素?cái)?shù)P,使得pd整除|G|).著名的Cayley定理告訴我們:任何一個(gè)有限群都與一個(gè)置換群(其右正則表示)同構(gòu).這一定理奠定了置換群在現(xiàn)代數(shù)學(xué)中的重要地位.近年來,基于O'Nan-Scott-Praeger定理的發(fā)現(xiàn)(見[30])和Liebeck, Praeger, Saxl得到的有限單群的極大因子分解(見[24]),置換群論的研究得到了快速的發(fā)展,并且在許多領(lǐng)域(尤其在代數(shù)圖論領(lǐng)域)發(fā)現(xiàn)了很好的應(yīng)用.2005年,Dietrich和Erick [8]研究了立方自由階群的性質(zhì),利用其結(jié)果,Li和Qiao[35]完全確定了立方自由階群的結(jié)構(gòu),進(jìn)而在后續(xù)文章[21]得到了四次自由階群的一些好的結(jié)構(gòu)性質(zhì).特別地,他們確定了所有立方自由階和四次自由階的非交換單群.本文的主要目的之一是研究五次自由階群的性質(zhì),特別地,得到五次自由階擬本原置換群的分類,并確定所有五次自由階非交換單群.注:一個(gè)置換群G ≤ Sym(Ω))稱為擬本原置換群如果其每個(gè)極小正規(guī)子群在腕上都是傳遞的.1938年,Fruchet證明了任何一個(gè)置換群都是一個(gè)圖的自同構(gòu)群,從而建立了置換群論和圖論間的密切聯(lián)系.本文的第二個(gè)工作是利用所得的五次自由階擬本原置換群的分類結(jié)果去分類具有頂點(diǎn)本原五次自由階自同構(gòu)群的所有三度弧傳遞圖r.具體而言,我們證明了下述之一成立:r≌K_4,K_4 - 4K_2或O_2 ( Petersen圖),或者r為PSL(2,p)的陪集圖,其中p≡±1 (mod 16)為素?cái)?shù).
[Abstract]:This paper aims to study the three degree Symmetric Graphs of the five free order quasi primitive permutation groups and their associations (Note: a replacement group G is called the replacement group of the D order of freedom, where D is a positive integer, if there is no prime number P, so that PD is divided into |G|). The famous Cayley theorem tells us what a finite group is all with a replacement group (its right regular representation). Isomorphism, which establishes the important position of displacement groups in modern mathematics. In recent years, the research on the maximal factorization of finite groups (see [24]) based on the discovery of the O'Nan-Scott-Praeger theorem (see [30]) and Liebeck, Praeger and Saxl (see [24]) has developed rapidly, and in many fields (especially in algebraic graph theory) Domain) found a good application in.2005 years. Dietrich and Erick [8] studied the properties of cubic free order groups. Using the results, Li and Qiao[35] completely determined the structure of the cubic free order group. Then, in the subsequent article [21], some good structural properties of the four order free order groups were obtained. In particular, they determined all cubic free order and four. One of the main purposes of this paper is to study the properties of the five order free order group. In particular, we obtain the classification of the five order quasi primitive permutation groups and determine all five free order noncommutative groups. Note: a replacement group G < Sym (omega)) is called the quasi primitive permutation group if each minimal normal subgroup is on the wrist. In all the.1938 years of transfer, Fruchet proves that any substitution group is an automorphism group of a graph, and thus establishes the close relation between the permutation group theory and the graph theory. The second work of this paper is to classify the five free order primitive permutation groups by using the results to classify the groups with the vertex primitive five order free order automorphism groups With three degrees of arc transitive graph R., we prove that one of the following is established: R K_4, K_4 - 4K_2 or O_2 (Petersen graph), or R is a coset graph of PSL (2, P), in which p + 1 (MOD 16) is a prime.

【學(xué)位授予單位】：云南財(cái)經(jīng)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O157.5

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 潘江敏;丁素云;劉寅;;有限素?cái)?shù)度弧正則圖[J];中國科學(xué):數(shù)學(xué);2014年03期

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本文編號(hào)：1795344