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On the basis of the quasi-isomorphism of finite groups, a new mapping, weak isomorphism, from a finite group to another finite group is defined. Let G and H be two finite groups and G be weak-isomorphic to H. Then G≌H if G satisfies one of the following conditions. 1) G is a finite Abelian group. 2) The order of G is p^3. 3 ) The order of G is p^n+1 and G has a cyclic normal subgroup N = 〈a〉 of order p^n. 4) G is a nilpotent group and if p^││G│, then for any P ∈ Sylp (G), P has a cyclic maximal subgroup, where p is a prime; 5) G is a maximal class group of order p4(p〉3). 相似文献
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