摘要
n阶有限群G可以嵌入n次对称群Sn.于是对于给定任意一个从G到Sn的同态映射,可以根据G中元素在这个映射之下的像来定义该元素的奇偶性.那么有一个基本问题,就是G中同一个元素在不同的同态映射之下是否具有相同的奇偶性.在本文中,主要研究G为Abel群的情形.
A finite group G of order n can be embedded into the symmetric group Sn.Given any homomorphism of G into Sn, the elements of G can be divided into odd ones and even ones according their image in Sn.Then we have an elementary question that whether the same element has the same parity under different homomorphisms.In this paper, we will discuss this problem parity in finite Abel groups.
出处
《内蒙古民族大学学报（自然科学版）》
2009年第2期136-138,共3页
Journal of Inner Mongolia Minzu University：Natural Sciences
基金
内蒙古民族大学硕士科研基金项目(2006049)
关键词
有限群
置换
奇偶性
Finite groups
Permutation
Parity
