半正规、C-正规与有限群的超可解性

Semi-Normal,C-Normal and Supersolvability of Finite Groups

把半正规与 C-正规结合起来 ,证明若群 G的每个 Sylow子群的极大子群在 G中或半正规或 C-正规 ,则 G超可解 .并结合半正规与 C-正规的概念得到了有限群超可解的若干充分条件 ,同时推广了一些已知结果 .

In combination of the concepts of semi normal subgroup and C normal subgroup,it is proved that G is supersolvable if the maximal subgroup of each Sylow subgroup of G is semi normal or C normal in G. Some sufficient conditions are obtained for finite groups to be supersolvable. Some previously known results are generalized.