【摘要】 证明了一个有限群G如果只有4个子群满足幂条件,那么G≌Z3×Z3.同时还证明了一个有限群G如果只有5个子群不满足幂条件,那么群G≌Z2×Z4或G≌D8或G≌Gk,Gk=〈a,b｜a5=b2n=1,b-1ab=ak,k=2,3,4,b2a=ab2〉.更多还原

【Abstract】 In this paper, we have proved that if a finite group G with 4 subgroups not satisfying exponent condition, then G≌Z₃×Z₃ or G≌Z₂×Z₄, meanwhile, we also proved that: if a finite group G with 5 subgroups not satisfying exponent condition, then G≌Z₂×Z₄ or G≌D₈ or G≌G_k, G_k=<a, b|a⁵=b²ⁿ=1, b^-1ab=a^k, k=2,3,4, b²a=ab²>.更多还原