ISSN:
1572-9192
Keywords:
difference set
;
representation theory
;
abelian group
;
nonabelian group
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Nontrivial difference sets in groups of order a power of 2 are part of the family of difference sets called Menon difference sets (or Hadamard), and they have parameters (22d+2, 22d+1±2 d , 22d ±2 d ). In the abelian case, the group has a difference set if and only if the exponent of the group is less than or equal to 2 d+2. In [14], the authors construct a difference set in a nonabelian group of order 64 and exponent 32. This paper generalizes that result to show that there is a difference set in a nonabelian group of order 22d+2 with exponent 2 d+3. We use representation theory to prove that the group has a difference set, and this shows that representation theory can be used to verify a construction similar to the use of character theory in the abelian case.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1022446822561
Permalink