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2017•Pure MathematicsOpen access

The Automorphism Group of A Class of Abelian p-Group

树珍 方

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Abstract

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.

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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.

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Available abstract

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.

Key concepts: p-group, Abelian group, Mathematics, Alternating group, Inner automorphism, Non-abelian group, G-module, Group (periodic table)

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