a subgroup $h$ is said to be $nc$-supplemented in a group $g$ if there exists a subgroup $kleq g$ such that $hklhd g$ and $hcap k$ is contained in $h_{g}$, the core of $h$ in $g$. we characterize the supersolubility of finite groups $g$ with that every maximal subgroup of the sylow subgroups is $nc$-supplemented in $g$.

The maximality of certain symplectic subgroups of unitary groups PSUn(K), n ≥ 4, (K any field admitting a non–trivial involutory automorphism) belonging to the class C5 of Aschbacher is proved. Furthermore some related geometry in the case n = 4 and K finite is investigated. Mathematics Subject Classification (2002): 20G40, 20G28

This paper seeks to prove some results stated in [5], namely a statement of the Mobius function of PSL2(2 ), e > 1. These results extend P. Hall's calculation in [6] of the Mobius function of PSL2(/?) for any prime/?. The techniques used in the present paper (see especially §2) should be of use for evaluating the Mobius function fiG for other classical groups G; in fact for the case when G = ?S...