【摘要】 若G为An的子群,则O(G)|O(An),但m|n!/2时,An不一定存在m阶子群。已经证明了当m≤n时,An一定具有m阶了群,通过直接构造An的子群的办法.将上述结果作了进一步的推广,证明了m, N0(m),使得当n>N0(m)时,An存在m阶子群.更多还原

【Abstract】 IF G is a subgroup of An , the O ( G) | O(An) , but if m |n!/2 , there may not necessarily be an m-ordersubgroup. It has been proved that .An an must have an m-order subgroup when m ≤ n . The result mentioned a-bove has been further generalized by directly contructing the subgroup of An .and it has been proved that A m , N0 ( m ) so that when n > N0 ( m ) ,An has an m-order subgroup.更多还原