置换群关于变换后基的强生成集的算法

A Algorithm for Finding a Strong Generating Set of a Permutation Group Relative to a Changed Base

本文给出置换群关于变换后的基的强生成集的一种算法及其理论证明,并讨论了既约强生成集和最小强生成集的问题。

Let X = α1,α1,… ,αk be a base of a permutation group G. Let A be a strong generating set of G relative to X. Set X=β1,β2,…,βk. where βj = αj+1,βj+1=αj and βi =αi if i≠j,j=1, then X is also a base of G. A algorithm for finding a strong generating set of G relative to X is given in this paper. The concepts of a reduced strong generating set and a least strong generating set are also discussed.