论60阶群的构造

On the Structures of Groups of Order 60

设G是60阶群,那么G共有11个互不同构的类型,其中Sylow 5-子群正规的有10个。由此可得60阶单群A5的一个新的刻划,即60阶群是单群的充要条件是它的Sylow 5-子群不正规。

Let G be groups of order 60.In this paper,we have showed that G has 11 nonisomorphic structures,and there are 10 structures among these where its Sylow 5-subgroups are normal.Thus we can know a new characterization of the simple A5,i.e.the group of order 60 is simple if and only if its Sylow 5-subgroups are non-normal.