【摘要】 本文仅用“群的阶”、“元的阶”来刻划60阶单群A₅^-,即A₅^-的特征性质是:（1）群的阶至少含三个相异的质因子;（2）群中异于1的每元的阶均为质数.此外,本文还得出有限质元群的下述分类:1)qⁿ阶群;2)pqⁿ阶群;3)A₅^-.更多还原

【Abstract】 In this paper, we characterize A5, the simple group of order 60, with the order of the group and the orders of its elements as the only conditions. That is, the characteristic property of A5 is.(1) the order of the group contains at least three different prime factors;(2) the order of every non-identity element in the group is a prime. In addition, we have obtained the following classification of thefinite groups in which every element has prime order:1) the groups of order qn;2) the groups of order pqn;3) A5.更多还原