In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained critical conditions on existence of a unique solution, infinitely many solutions or nonexistence any solution for the two classes algebraic equation.
本文运用广义四元数代数的矩阵表示讨论了两类广义四元数的一次代数方程的解问题 ,并得到了这两类代数方程有唯一解、无穷多解、无解的判别条件。
In this note, we show that for any two matrices A and B over a generalized quaternion algebra denned on an arbitrary field F of characteristic not equal to two, if A and B are similar and the main diagonal elements of A and B are in.
本文对于特征不是2的任意域F上定义的广义四元数代数上的两个矩阵A和B,给出如果A和B相似并且它们的主对角线上的元素在F中,那么它们的迹相等。
This paper perfectly resolves the CI property,normality and arc-transitive property of connected Cayley graphs of valencies 4 and 5 on generalized quaternion groups Q4pm(p is odd prime,m is positive integer).
完整解决了广义四元数群Q4pm(p为奇素数,m为正整数)的连通4度及5度无向Cayley图的CI性、正规性和弧传递性。
A group G is said to be a generalized quaternion groups,if Q4 n =<a,b│a2n=1,b2=an.
一个有限群称为广义四元数群,若Q4n=
A group G is said to be a generalized quaternion groups,if Q_(4p)=〈a,b|a~(2n)=1,b~2=a~n,a~b=a~(-1)〉,p3.
一个有限群称为广义四元数群,若Q4n=〈a,b a2n=1,b2=an,ab=a-1,〉n 3。