摘要
For a maximal subgroup M of a finite group G, the normal index of M is defined to be the order of a chief factor H/K, where H is minimal supplement of M in G. For A【G , if there are two normal subgroup L and J of G such that G = A·L and A∩L= J, we say that A is an almost normal subgroup in G. We obtain several results that G to be solvable and supersolvable.
For a maximal subgroup M of a finite group G, the normal index of M is defined to be the order of a chief factor H/K, where H is minimal supplement of M in G. For A<G , if there are two normal subgroup L and J of G such that G = A·L and A∩L= J, we say that A is an almost normal subgroup in G. We obtain several results that G to be solvable and supersolvable.
