Abstract: The influence of U-supplemented subgroups on the structure of finite groups was investigated. Some conditions of p-nilpotency under assumption that some primary subgroups (for example, 2-maximal subgroups of Sylow subgroup) are U-supplemented were established. Meanwhile, some new characterizations of a group belonging to a given formation of finite groups were obtained. As an application, a series of previously known results are unified and generalized.

Key words: U-supplemented, p-nilpotent, Sylow p-subgroup