机构地区: 广西师范学院数学与计算机科学系
出 处: 《四川师范大学学报(自然科学版)》 2008年第5期522-525,共4页
摘 要: 设G1,G2是群,映射f:G1→G2叫做G1到G2的广义同态映射,如果a,b∈G1,等式(ab)f=afbf和(ab)f=bfaf至少有一个成立.利用广义同态映射,以统一的观点处理互为对称的同态映射与反同态映射,所得相关结果在一定程度上揭示了广义自同构与有限群结构的联系. Given groups G1 and G2 , a mapping f: G1 → G2 is said to be a generalized homomorphism from G1 to G2 if for any a, b in G1 , either ( ab )^f = a^fb^for ( ab )^f =b^fa^f. By using the concept of generalized homomorphism, we uniformly deal with homomorphisms and anti-homomorphisms in a unified view and obain some related results, which uncover the relation between the generalized automorphisms and the structure of finite groups in a way.