﻿ 一类交换p-群的自同构群

# 一类交换p-群的自同构群The Automorphism Group of A Class of Abelian p-Group

Cpβipβi 阶的循环群，其中p 为素数，1i≤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× CpnCpβ1× 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 1i≤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.

[1] Bidwell, J.N.S. (2006) Computing Automorphisms of Finite Groups. Ph.D. Thesis, University of Otago, Dunedin.

[2] Bidwell, J.N.S., Curran, M.J. and McCaughan, D.J. (2006) Automorphisms of Direct Products of Finite Groups. Archiv der Mathematik, 86, 481-489. https://doi.org/10.1007/s00013-005-1547-z

[3] Bidwell, J.N.S. (2008) Automorphisms of Direct Products of Finite II. Archiv der Mathematik, 91, 111-121. https://doi.org/10.1007/s00013-008-2653-5

[4] 周芳, 马玉杰, 刘合国. 半直积的稳定自同构群[J]. 数学进展, 2010, 39(6): 673-678.

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