群同态个数的刻画

Abstract

Abstract: By using the equivalence class of group action, the set of cocycles and the group homomorphism were connected. By characterizing the number of homomorphisms between two finite groups through the set of cocycles, we proved that for any finite groups A,G, if the number of elements in the set of cocycles of A and G could be divided by the greatest common divisor of |A| and |G|, the number of homomorphisms between A and G could be divided by the greatest common divisor of |A| and |G|.

Key words: cocycle, group action, homomorphism, finite group

CLC Number:

O152.1

LI Qingfeng, HAI Jinke. Characterization of Number of Group Homomorphisms[J].Journal of Jilin University Science Edition, 2019, 57(1): 32-36.

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Characterization of Number of Group Homomorphisms

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