一类非交换群的自同态和自同构数量

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

基于群理论下一类非交换群的群结构以及元素的阶,计算一类Sylow p-子群为循环群的2qp^(n)(q<p为奇素数)阶非交换群的自同态个数和自同构个数,并验证其自同态个数满足T.Asai和T.Yoshida猜想。

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 2qp^(n)whose Sylow p-subgroups is cyclic is calculated,where q<p 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.