中文摘要：

利用中心以外的非循环子群自正规化性质, 刻画了有限群的结构, 得到： 如果对于有限群G 的每个素数幂阶非循环子群H, 或者H ≤ Z（G）, 或者｜NG（H） ： H｜ ≤ 2, 则G 是超可解群.对于任意非循环非中心子群H 满足NG（H） = H 的有限群G, 给出了它的结构分类.

英文摘要：

By some non-cyclic subgroups outside centre being self-normalizing to characterize the structure of finitegroups, the results were obtained as follows： A finite group G is always supersolvable if either ｜NG（H） ： H｜ ≤ 2 orH ≤ Z（G） for every non-cyclic subgroup H of G of prime-power order. Also, finite groups G with all non-cyclicsubgroups being self-normalizing or contained in Z（G） are completely classified.