On the covering number of symmetric groups having degree divisible by six

If a group G is the union of proper subgroups H-1, ..., H-k, we say that the collection {H-1, ..., H-k} is a cover of G, and the size of a minimal cover (supposing one exists) is the covering number of G, denoted by sigma(G). Maroti showed that sigma(S-n) = 2(n-1) for n odd and sufficiently large, and he also gave asymptotic bounds for n even. In this paper, we determine the exact value of sigma(S-n) when n is divisible by six. (C) 2016 Elsevier B.V. All rights reserved.