用不可补子群个数刻画单群A₅
Characterizing the Simple Group A₅ by the Number of Uncomplemented Subgroups

设G是有限群，H≤G.如果G中存在子群K≤G，满足G=KH，且H∩K=1，那么称H在G中可补.研究子群的可补性对有限群结构和性质的影响是群论研究中十分重要的课题.给出了5次交错群A₅的一个新刻画，即60阶群G？A₅的充分必要条件是G中只有46个不可补子群.
Let G be a finite group, H≤G. If there exists a subgroup K of G such that G=HK and H∩K=1, then H is called complemented in G. The subgroup's complementarity on the structure and properties of finite groups is a very important topic in group theory. A new characterization of the alternating group A₅ is given, i.e., let G be a group of order 60, G？A₅ if and only if G only has 46 uncomplemented subgroups