JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (2): 101-105.doi: 10.6040/j.issn.1671-9352.0.2018.048

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T.Asai and T.Yoshida problem of group homomorphism

ZHAO Yan-wei, HAI Jin-ke*   

  1. College of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong, China
  • Published:2019-02-25

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Abstract: Let A and G be finite groups, A=A1×A2. Suppose that A1/A'1, A2/A'2 meet certain conditions, where A'1, A'2 are the derived group A1, A2 respectively. The number of homomorphisms from A to G is divisible by the greatest common divisor of |A/A'| and |G| is proved, the conjecture of Asai and Yohsida is true.

Key words: group homomorphism, group action, cyclic group

CLC Number: 

  • O152.1
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