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中文摘要：
利用X-可换子群的概念，得到了有限群超可解的2个充分条件：（1）设G是可解群，石是G的子集且包含G的极小子群和极大子群。如果G的每个极大子群和G的sylow子群的每个极大子群在G中X-可换，那么G是超可解群；（2）设足签，X是G的子集且包含G的p-子群。如果每个不包含K的G的极大子群在G中X-可换，那么K是超可解群。
英文摘要：
Using the concept, X-permutable subgroup of finite groups, two sufficient conditions of supersoluble groups are obtained：（1） G is a soluble group, let X be a subgroup of G such that X contains every maximal subgroup and every minimal subgroup of G.Suppose that every maximal subgroup of G is X-permutable with every maximal subgroup of every Sylow subgroup of G in G, then G is a supersoluble group;（2）Let K be a normal subgroup of G, let X be a subgroup of G such that X contains every p-subgroup of G. Suppose that every maximal subgroup of G not containing K is X-permutable in G, then K is a supersoluble group.
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The structure of finite non-nilpotent groups in which every 2-maximal subgroup permutes with all 3-m
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