【摘要】 定义任意群的本质子群、多余子群,并给出它们关于群的交、积、直积等运算的性质.设S(G)是群G的所有本质子群的交,R(G)是群G的所有多余子群的积,证明S(G)是G的所有单的正规子群的积,R(G)是G的所有极大正规子群的交。更多还原

【Abstract】 Essential subgroups and superfluous subgroups of a group are defined,and their prop-erties in joint,product,direct product operations between groups are given.Let S(G) be the joint of the essential subgroups of a group G,and R(G) be the product of the superfluous subgroups of the group G.It is proved that S(G) is the product of the simple normal subgroups of the group G,and R(G) is the joint of the maximal normal subgroups of the group G.更多还原