On the nonexistence of semi-regular relative difference sets

• المؤلفون الرئيسيون: Leung, Ka Hin, Schmidt, Bernhard, Zhang, Tao
• مؤلفون آخرون: School of Physical and Mathematical Sciences
• التنسيق: مقال
• اللغة: English
• منشور في: 2023
• الموضوعات: Science::Mathematics; Group Ring; Weil Number
• الوصول للمادة أونلاين: https://hdl.handle.net/10356/170341
• المؤسسة: Nanyang Technological University

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.