On the existence of difference sets in groups of order 96

  title={On the existence of difference sets in groups of order 96},
  author={Anka Golemac and Josko Mandic and Tanja Vucicic},
  journal={Discret. Math.},
The correspondence between a (96,20,4) symmetric design having regular automorphism group and a difference set with the same parameters has been used to obtain difference sets in groups of order 96. Starting from eight such symmetric designs constructed by the tactical decomposition method, 55 inequivalent (96,20,4) difference sets are distinguished. Thereby the existence of difference sets in 22 nonabelian groups of order 96 is proved. 

Topics from this paper

Graphs and symmetric designs corresponding to difference sets in groups of order 96
Using the list of 2607 so far constructed (96,20,4) difference sets as a source, we checked the related symmetric designs upon isomorphism and analyzed their full automorphism groups. New (96,20,4,4)Expand
An algorithm for enumerating difference sets
The DifSets package for GAP implements an algorithm for enumerating all difference sets in a group up to equivalence and provides access to a library of results that can be dramatically decreased and searches of groups of relatively large order can be completed. Expand
Nonabelian Groups with (96, 20, 4) Difference Sets
Of the 231 groups of order 96, 90 groups admit $(96,20,4)$ difference sets and 90 groups do not, and the ninety groups with difference sets provide many genuinely nonabelian difference sets. Expand
New Regular Partial Difference Sets and Strongly Regular Graphs with Parameters (96, 20, 4, 4) and (96, 19, 2, 4)
New (96,20,4,4) and (96,19,2,4) regular partial difference sets are constructed, together with the corresponding strongly regular graphs. Our source are (96,20,4) regular symmetric designs.
All (96, 20, 4) difference sets and related structures
The completion of the search for all $(96,20,4)$ difference sets is announced, relying on the computer software GAP and the work of numerous authors over the last few decades. Expand


New difference sets in nonabelian groups of order 100
In two groups of order 100 new difference sets are constructed. The existence of a difference set in one of them has not been known. The correspondence between a (100, 45, 20) symmetric design havingExpand
New symmetric designs and nonabelian difference sets with parameters(100, 45, 20)
Six nonisomorphic new symmetric designs with parameters (100, 45, 20) are constructed by action of the Frobenius group E25 · Z12. This group proves to be their full automorphism group. Its FrobeniusExpand
Construction of new symmetric designs with parameters (70, 24, 8)
A construction of all symmetric designs with parameters (70,24,8) on which the group E 8 ∘ F 21 operates so that the automorphism of order 7 operates fixed-point-free. Expand
On a symmetric design (133,33,8) and the group E8 × F21 as its automorphism group
This article presents the examination of the possibility that group Eg' F21 operates on a symmetric design with parameters (133,33,8) as its automorphism group. The method based on coset enumerationExpand
Variations on a Scheme of McFarland for Noncyclic Difference Sets
  • J. Dillon
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 1985
The k-subset D of the group G of order u is called a (u, k, A, n)-difference set if every nonidentity element of G has exactly 1” representations as a difference of two elements of D; the parameter nExpand
Coset Enumeration in Groups and Constructions of Symmetric Designs
Publisher Summary This chapter discusses coset enumeration in groups and constructions of symmetric designs. It presents a group in terms of generators and relations so that each point or blockExpand
Some New Difference Sets
This paper constructs these difference sets, thereby filling a missing entry in Lander's table with the answer “yes,” and completes the existence status of (96, 20, 4) difference sets. Expand
A Family of Difference Sets in Non-cyclic Groups
  • R. McFarland
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 1973
A construction is given for difference sets in certain non-cyclic groups with the parameters v, k, λ, n, which has minus one as a multiplier for every prime power q and every positive integer s. Expand
A Unifying Construction for Difference Sets
We present a recursive construction for difference sets which unifies the Hadamard, McFarland, and Spence parameter families and deals with all abelian groups known to contain such difference sets.Expand
Construction of new symmetric designs with parameters (66,26,10)
It is known that there exists only one (Tran van Trung's) design for (66,26,10) up to now. In this article we consider designs for (66,26,10) with the Frobenius group F39 and we prove that thereExpand