一类交换p-群的自同构群
The Automorphism Group of A Class of Abelian p-Group
DOI: 10.12677/PM.2017.71004, PDF, HTML, XML, 下载: 1,564  浏览: 2,677  国家自然科学基金支持
作者: 方树珍, 周 芳：太原师范学院数学系，山西 晋中
关键词: 自同构群；循环群；矩阵表示；直积；Automorphism； Cyclic Group; Matrix Representation; Direct Product
摘要: 设Cpβi 是pβi 阶的循环群，其中p 为素数，1≤i≤4 。J. N. S. Bidwell利用矩阵表示方法得到了没有共同直因子的直积Cpm× Cpn和Cpβ1× Cpβ2× Cpβ3 的自同构群。本文采用同样的方法得到了直积Cpβ1× Cpβ2× Cpβ3×Cpβ4 的自同构群的生成元和生成关系。 Let Cpβi be the cyclic group of order pβi where p is a prime number, and 1≤i≤4 . Using matrix representation, J. N. S. Bidwell got the automorphisms of direct products Cpm× Cpn , and Cpβ1× Cpβ2× Cpβ3 which have no common direct factor. In this paper, the generators of the automorphism of direct product Cpβ1× Cpβ2× Cpβ3×Cpβ4 and the relations between them are obtained.
文章引用：方树珍, 周芳. 一类交换p-群的自同构群[J]. 理论数学, 2017, 7(1): 20-29. http://dx.doi.org/10.12677/PM.2017.71004

参考文献

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