S_n的元素阶的集合的两种刻画

Two Kinds of Descriptions for the Set of Orders of Elements in S_n

Sn是n次对称群,On是Sn的元素的阶的集合,完整地给出了On的两种刻画On={[n1,n2,…,ns]|n1,n2,…,ns为正整数且sum ni≤n from i=1 to s},On={Π i=1 w piαi|p1,p2,…,pw为互异素且Σi=1 w piαi≤n}.

In this paper,let Sn be the symmetric group of degree n and On be the set of orders of elements in Sn,the author completely gives two kinds of descriptions of OnOn={[n1,n2,…,ns]｜n1,n2,…,ns are positive integers and sum ni≤n from i=1 to s} On={Π i=1 w pαii｜p1,p2,…,pware distinct positive primes and Σi=1 w pαii≤n}