JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (2): 13-19.doi: 10.6040/j.issn.1671-9352.0.2022.058

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The number of endomorphisms and automorphisms of a class of non-abelian groups

ZHANG Wei1,2, GUO Ji-dong1,2*, ZHANG Liang1,2   

  1. 1. College of Mathematics and Statistics;
    2. Institute of Applied Mathematics, Yili Normal University, Yining 835000, Xinjiang, China
  • Published:2023-02-12

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Abstract: Based on the group structure and the order of elements of a class of non-abelian groups in group theory, the number of endomorphisms and automorphisms of a class of non-abelian groups of order 2qpn whose Sylow p-subgroups is cyclic is calculated, where q

and both are odd primes. Moreover, it is proved that the number of endomorphisms of such groups satisfies the conjecture of T. Asai and T. Yoshida in this case.

Key words: non-abelian group, endomorphism, automorphism, conjecture of T.Asai &, T.Yoshida

CLC Number: 

  • O152.6
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