Mohammad Javad Ataei - Department of Mathematics, Payame Noor University, Iran

Let G denotes a semisimple C۸-group and fMi j۱ i ۸g be a maximal irredundant ۸-cover for G, withcore-free intersection D =∩۸i=۱Mi. Also for each i, ۱ i ۸ we assume that jG : Mij = i such that(....)Let G be a Cn-group, we say that G is a core i۲-group if (Mi)G \ (Mj )G = ۱ for ۳ i < j ۸. Also let Gbe a Cn-group and core i۲-group, then we say that N := (M۱)G \ (M۲)G central core of G. In this paperwe show that if G be a semisimple C۸-group and l ۴ then G is core i-۲ group. Also we give some resultsfor central core of G.