~ study the existence of nontrivial (2m, k, X )-difference sets in dihedral groups. Some nonexistence results are proved. In particular, we show that n = k -3, is odd and Β’(n)/n < 112. Finally, a computer search shows that, except 5 undecided cases, no nontrivial difference set exists in dihedral gr
A note on difference sets in dihedral groups
β Scribed by Yingpu Deng
- Publisher
- Springer
- Year
- 2004
- Tongue
- English
- Weight
- 63 KB
- Volume
- 82
- Category
- Article
- ISSN
- 0003-889X
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π SIMILAR VOLUMES
We prove that for any primes p 1 ; . . . ; p s there are only finitely many numbers Q s iΒΌ1 p ai i ; a i 2 Z ΓΎ ; which can be orders of dihedral difference sets. We show that, with the possible exception of n ΒΌ 540; 225; there is no difference set of order n with 15n410 6 in any dihedral group.
Let D be a (v, k, \*)-difference set in a group G. Assume that G has a normal subgroup N such that GΓN is cyclic or nearly cyclic. Under the self-conjugacy assumption on exp(GΓN), we shall give bounds on |N| and \*. The theorem is applicable to a wider variety of parameters for groups, not necessari