(广义)四元数群的自同构群及其全形

The Automorphism Group and Holomorph of Quaternion Group(in generalized sense)

该文讨论了一类2n阶非交换群——(广义)四元数群Q2n=〈a,b|a2n-1=1,b2=a2n-2,b-1ab=a-1〉(n≥3)的自同构群A(Q2n)与全形H(Q2n)的置换表示,给出了A(Q2n)与H(Q2n)的构造.

This paper deals with the automorphism group A(Q_~2n ) and holomorph H(Q_~2n ) of quaternion group(in generalized sense) Q_~2n  of order 2n(n≥3). The structure and permutation representatives of A(Q_~2n ) and H(Q_~2n ) are given.