On the covering number of small symmetric groups and some sporadic simple groups
نویسندگان
چکیده
A set of proper subgroups is a covering for a group if its union is the whole group. The minimal number of subgroups needed to cover G is called the covering number of G, denoted by σ(G). Determining σ(G) is an open problem for many nonsolvable groups. For symmetric groups Sn, Maróti determined σ(Sn) for odd n with the exception of n = 9 and gave estimates for n even. In this paper we determine σ(Sn) for n = 8, 9, 10 and 12. In addition we find the covering number for the Mathieu group M12 and improve an estimate given by Holmes for the Janko group J1.
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عنوان ژورنال:
- Groups Complexity Cryptology
دوره 8 شماره
صفحات -
تاریخ انتشار 2016