A class of non-abelian 2-groups containing Menon difference sets |
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| Institution: | 1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;2. School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China;1. Rényi Institute, Budapest, Hungary;2. Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, PR China;1. College of Big Data Statistics, Guizhou University of Finance and Economics, Guiyang, Guizhou, 550025, China;2. Department of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197, USA;3. Department of Applied Mathematics, Northwestern Polytechnical University, Xi''an, Shaanxi 710129, China |
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| Abstract: | We show that every group in a certain class of 2-groups contains a Menon difference set. This provides further positive evidence for a conjecture of Dillon concerning 2-groups of order 22l which contain a normal subgroup isomorphic to Zl2. The conjecture, however, remains open. |
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