一类素数幂阶J群到其商群的同态个数

The Number of Homorphisms from a Class of Prime Power Order J-Groups to Its Quotient Group

给出了一类素数幂阶J群其元素的构造,讨论关于其换位子群作成的商群结构,建立该群到其商群的同态映射集合与商群自同态集合之间的同构映射,计算后者的数量满足T.Asai和T.Yoshida猜想,间接地验证前者的数量也满足该猜想.

The construction of the elements of a class of prime power-order J-groups is given,discusses the structure of the quotient group of J-groups by its commutator subgroup,establishes an isomorphism map between the set of J-group to its quotient group and the endomorphism set of the quotient group,calculates the number of the latter satisfies the conjectures of T.Asai and T.Yoshida,and indirectly verifies that the number of the former also satisfies the conjecture.