P-solvable Group Neutron Group Interactions And Related Topics

In this paper we research the basic property and the action on subgroup of solvable groups,in p-solvable groups we especially consider it in the case O_P'(G) = 1 in p-solvable groups. And we search the subgroup which can be normaled by p-subgroup in a group. In the end we research the problem of " decomposition " of groups, that is a problem how to represent a given group by the multiplication of subgroup or by the generation of several groups which have special property.