Let G be a finite group. A covering of G is a set of proper subgroups, whose union is equal to G. The least number of covering is denoted by σ(G) and a covering of cardinality σ(G) is called a minimal covering. In this paper, we investigate the minimal covering of symmetric group of degree nine, S_9. In finding the minimal covering of a group, we only need to consider the number of maximal subgroups of a group. We used Group Algorithm Programming (GAP) to find the conjugacy classes of maximal subgroups for S_9. In order to determine the minimal covering of S_9, it suffices to find a minimal covering of maximal cyclic subgroups by maximal subgroups of S9. We give a proof that 242 ≤ σ( S_9) ≤ 256.
展开▼
