摘要
一般域上线性群的自同构问题已经清楚了,本文对一个欧氏环上二阶线性群的自同构问题,给出具体结果。§1.
In this paper, for Euclidean ring R={(m+n2^(1/5))/2}, the automorphisms of PSL_2(R)and SL_2(R)and PGL_2(R)are decided concretely: (ⅰ) the identity map, (ⅱ) the automorphism is induced by an automorphism a→a~σ of R. However, there are the following two types of automorphisms of GL_2(R):(ⅰ)(T, S, K, U, Q, V)→(PTP^(-1), PSP^(-1), PKP^(-1), PUP^(-1), P(±Q) p^(-1), P(xV) P^(-1)), where x=±1, ±e^(-1), P∈GL_2(R); (ⅱ)(T, S, K, U, Q, V)→(PTP^(-1), PSP^(-1), PKP^(-1), PTUP^(-1), P(±Q)P^(-1), P(xQV)P^(-1)), where x=±1, ±e, P∈GL_2(R).
出处
《北京师范大学学报（自然科学版）》
CAS
1983年第2期29-36,共8页
Journal of Beijing Normal University(Natural Science)
