会议 ID：520 581 395

会议密码：012521

邀请人：许宝刚教授

摘要：Let G be an abelian group of order v.  A Steiner quadruple system of order v (SQS(v)) (G, B) is called symmetric K-invariant if for each B∈B, it holds that B+g∈B for each g∈G and B=-B+g’ for some g’∈G. When the Sylow 2-subgroup of G is cyclic, Munemasa and Sawa gave a necessary and sufficient condition for the existence of a symmetric G-invariant SQS(v) (2012), which is a generalization of a necessary and sufficient condition for the existence of a symmetric cyclic SQS(v) by Piotrowski (1985). In this talk, we give that a symmetric G-invariant SQS(v) exists if and only if v≡ 2,4 mod 6, the order of each element of G is not divisible by 8 and there exists a symmetric cyclic SQS(2p) for any odd prime divisor p of v.