On the nonexistence of semi-regular relative difference sets
In this paper, we study semi-regular relative difference sets. We give some nonexistence results on abelian (mn,n,mn,m) relative difference sets. In particular, we focus on the case when m is prime and show that, for any fixed integer n≥2, there are at most finitely many primes p for which an abelia...
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| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/170341 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | In this paper, we study semi-regular relative difference sets. We give some nonexistence results on abelian (mn,n,mn,m) relative difference sets. In particular, we focus on the case when m is prime and show that, for any fixed integer n≥2, there are at most finitely many primes p for which an abelian (pn,n,pn,p) relative difference set may exist. We illustrate our results by investigating the existence of (mn,n,mn,m) relative difference sets with m∈{2,3,4} in detail. |
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