本文關(guān)鍵詞：利用元素階之和及最高階刻畫群　出處：《西南大學》2015年碩士論文　論文類型：學位論文

  更多相關(guān)文章： 有限群 單群 最高階

【摘要】：眾所周知,有限單群是構(gòu)成有限群的基石,因此利用較為直觀和淺顯的性質(zhì)來刻畫有限單群,對于我們深入了解它們的性質(zhì)和結(jié)構(gòu)是大有裨益的.在本文中,我們主要考慮用元素的最高階及元素階之和刻畫有限單群.記m(G)為群G中元素的最高階,ψ(G)為群G中所有元素階之和,得到的主要結(jié)論如下：定理3.4階最小的非交換單群A5可以由m(G)和ψ(G)刻畫,即：G(?)A5當且僅當ψ(G)=ψ(A5)=211,m(G)=m(A5)=5.定理4.8階次小的非交換單群PSL(2,7)可以由m(G)和ψ(G)刻畫,即：G(?)PSL(2,7)當且僅當ψ(G)=ψ(PSL(2,7))=715,m(G)=m(PSL(2,7))= 7.
[Abstract]:It is well known that finite simple groups are the foundation stone of forming finite groups, so it is helpful for us to deeply understand their properties and structures by using more intuitive and simple properties to characterize finite simple groups. We mainly consider characterizing finite simple groups by the sum of the highest order of elements and the sum of order of elements. Let mG be the highest order of elements in group G and 蠄 G be the sum of the order of all elements in group G. The main results are as follows: theorem 3.4 the smallest noncommutative simple group A _ 5 can be characterized by MJ G) and 蠄 G), that is, the minimum noncommutative simple group A _ 5 of order 3.4. A5 if and only if 蠄 G ~ G = 蠄 ~ A _ 5 ~ (211m) ~ (?) A ~ (5). Theorem 4 ~ (th) small nonabelian simple group PSL(2 of order 4.8. 7) can be described by MJ G) and 蠄 G). If and only if 蠄 ~ (G) = 蠄 ~ (?) PSL ~ (2 / 7) = 7 ~ (7) ~ 715m ~ (~ (?) ~ (?) ~ ~ ~ (
【學位授予單位】：西南大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O152.1

【參考文獻】

相關(guān)期刊論文 前2條

1 施武杰;A_5的一個特征性質(zhì)[J];西南師范大學學報(自然科學版);1986年03期

2 施武杰;Pure Quantitative Characterization of Finite Simple Groups (Ⅰ)[J];Progress in Natural Science;1994年03期

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本文編號：1433565