中心以外的非循环子群自正规化的有限群

Finite groups with some non-cyclic subgroups outside centre being self-normalizing

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|N_G(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N_G(H)=H的有限群G,给出了它的结构分类。

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.