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中文摘要：
设G1，G2是群，映射f：G1→G2叫做G1到G2的广义同态映射，如果任意a，b∈G1，等式（ab）^f=a^fb^f和（ab）^f=b^fa^f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．
英文摘要：
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.
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