利用元素阶之和及最高阶刻画群

发布时间：2018-01-16 14:41

本文关键词：利用元素阶之和及最高阶刻画群　出处：《西南大学》2015年硕士论文　论文类型：学位论文

【摘要】：众所周知,有限单群是构成有限群的基石,因此利用较为直观和浅显的性质来刻画有限单群,对于我们深入了解它们的性质和结构是大有裨益的.在本文中,我们主要考虑用元素的最高阶及元素阶之和刻画有限单群.记m(G)为群G中元素的最高阶,ψ(G)为群G中所有元素阶之和,得到的主要结论如下：定理3.4阶最小的非交换单群A5可以由m(G)和ψ(G)刻画,即：G(?)A5当且仅当ψ(G)=ψ(A5)=211,m(G)=m(A5)=5.定理4.8阶次小的非交换单群PSL(2,7)可以由m(G)和ψ(G)刻画,即：G(?)PSL(2,7)当且仅当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 ~ (~ (?) ~ (?) ~ ~ ~ (
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O152.1

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