JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (12): 59-62.doi: 10.6040/j.issn.1671-9352.0.2019.092

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Number of homomorphisms between groups with Abel direct factors and finite groups

LI Ning-ying1, GUO Ji-dong1*, HAI Jin-ke1,2   

  1. 1. College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China;
    2. College of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong, China
  • Published:2019-12-11

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Abstract: Let H,G be finite group. If the subgroup A of H is an Abel direct factor of H, then the number of homomorphism from H to G is a multiple of the largest common factor of |A| and |G|. The famous T.Yoshidas theorem is generalized.

Key words: congruence, direct factor, group homomorphism

CLC Number: 

  • O152.1
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