【摘要】 利用完全初等的方法刻画交错群A₅和对称群S₅.得到如下结论:若群G的阶为60,则G?A₅的充要条件是G的交换子群的阶为2,3,4,5,且个数分别是15,10,5,6;若群G的阶为120,则G?S₅的充要条件是G的交换子群的阶为2,3,4,5,6,且个数分别是25,10,35,6,10.更多还原

【Abstract】 It is proved that A₅ and S₅ can be uniquely determined by its order and the numbers of its abelian subgroups of different orders by elementary approaches. The conclusions are as following: If the order of group G is 60, then G?A₅ if and only if the orders of the abelian subgroups of G are 2,3,4,5 and the numbers of them are 15,10,5,6 respectively; If the order of group G is 120, then G?S₅ if and only if the orders of the abelian subgroups of G are 2,3,4,5,6, and the numbers of them are 25,10,35,6,10 respectively.更多还原