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Extraneous Multipliers of Abelian Difference Sets
| Content Provider | Scilit |
|---|---|
| Author | Wei, Wan-Di Gao, Shuhong Xiang, Qing |
| Copyright Year | 2020 |
| Description | Let (G,·) be a group of order v. A k-subset D of G is called a (v,k,λ) difference set if the list of differences d 1 d 2 − 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003071907/4aa30375-4cd4-4e51-84c6-8c4f8af96c27/content/eq1689.tif"/> , $d_{1},d_{2}$ ∈ G, contains each non-identity element of G exactly λ times. The difference set D is said to be abelian (resp. cyclic) if G is abelian (resp. cyclic). The number n = k − λ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003071907/4aa30375-4cd4-4e51-84c6-8c4f8af96c27/content/eq1690.tif"/> is called the order of the difference set. An automorphism α of G is called a multiplier of D if D α = aDb https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003071907/4aa30375-4cd4-4e51-84c6-8c4f8af96c27/content/eq1691.tif"/> for some a,b ∈ G. When a is the identity element, α is called a right multiplier. Let G be abelian. We know that for any positive integer t relatively prime to v, the mapping x ↦ x t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003071907/4aa30375-4cd4-4e51-84c6-8c4f8af96c27/content/eq1692.tif"/> is an automorphism of G. If it happens to be a multiplier of D, then it is called a numerical multiplier of D. In this case we sometimes say that t is a multiplier by abuse of terminology. The following theorem suggests that the factors of n are an 166important source of multipliers of an abelian difference set of order n. |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2006-0-13813-1&isbn=9781003071907&format=googlePreviewPdf |
| Ending Page | 173 |
| Page Count | 9 |
| Starting Page | 165 |
| DOI | 10.1201/9781003071907-15 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2020-12-22 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Combinatorial Designs and Applications Automorphism Called Identity Element Abelian Difference Sets Multipliers of Abelian |
| Content Type | Text |
| Resource Type | Chapter |
