局部化的M-可补子群对群构造的影响

Influence of Localized M-Supplemented Subgroups on Structure of Finite Groups

假设群G的一个Sylowp-子群P的子群D满足1<D≤P,p是G的素因子.利用P的每个阶为D子群在P的正规化子NG(P)中的M-可补性质,并结合H(P)={H≤P P′≤H≤Φ(P)}中子群的弱s-可补性质,得到了刻画p-幂零群和p-超可解群新的充分条件.

We supposed that a subgroup Dof a Sylowp-subgroup Pof a group Gsatisfied 1D≤P,where p was a prime divisor of G.The new sufficient conditions for the characterization of p-nilpotent groups and p-supersolvable groups were obtained by using M-supplemented property of each order of D subgroup in the normalizer NG（P）of Pand combining the weakly s-supplemented property of H（P）={H≤P P′≤H≤Φ（P）}.