最高阶元的阶为7及Sylow 2-子群的阶为8的有限群的结构

摘要

设G 是有限群,由于有限单群可以由群的阶和元素的阶集合刻画,那么减少一些数量作为条件是否仍然可以刻画有限单群?基于此,从L2(7)的最高阶元的阶和Sylow 2-子群的阶出发,即当群G 的最高阶元的阶为7及Sylow 2-子群的阶为8时,不能刻画L2(7),但可以得到群G 的所有结构.%Let Gbe a finite group,because of a finite simple group using the order of Gand the set of orders of elements in G,then reducing the number of conditions and whether or not can describe finite simple groups.Based on this,we starting in this paper from the Sylow 2-subgroup and the order of the largest element of L2(7),this is,the largest element order is 7and Sylow 2-subgroup order is 8of G,here L2(7) can not be portrayed,but we obtain all the characterize of G.