hamidreza dorbidi

Let G be a group. An irredundant n-covering of a group is a finite set of n proper such subgroups of G is the union of Hi but G is not union of n-1 of H_i. Let Σ(G) = {n in N:There is an irredundant n-covering of G}. Then \sigma(G) = min Σ(G) is called the covering number of G. It is well known that for any group G we have 2 not in Σ(G) We prove that for any n >3 there is a group G such that n is in Σ(G). Also we prove that a covering of the Galois group of an extension E/F gives a sum decomposition of E. Also we have a decomposition of group rings RG = RH1 + ... + RHn.