Volume 30 • Number 1 • 2007   • The Symmetric Group of Degree Six can be Covered by 13 and no Fewer Proper Subgroups A. Abdollahi, F. Ashraf and S. M. Shaker Abstract. In this note, we prove that the symmetric group of degree six can be covered by 13 and no fewer proper subgroups. This partially answers a question of M. J. Tomkinson [Groups as the union of proper subgroups, Math. Scand. 81(1997), 189--198] and gives a negative answer to a part of a conjecture of L. Serena [On finite covers of groups by subgroups, Advances in group theory 2002, 173--190, Aracne, Rome, 2003]. 2000 Mathematics Subject Classification: 20D60. Full text: PDF