منابع مشابه
On non-Abelian group difference sets
This paper is motivated by R. H. Bruck’s paper[3], in which he proved that the existence of cyclic projective plane of order n ≡ 1 (mod 3) implies that of a non-planar difference set of the same order by proving that such a cyclic projective plane admits a regular non-Abelian automorphism group using n as a multiplier. In this paper we will discuss in detail the possibility of using multipliers...
متن کاملNon-Abelian Hadamard Difference Sets
Difference sets wi th pa rame te r s (v, k, 2) m a y exist even if there are no abelian (v, k, ,~) difference sets; we give the first k n o w n example of this s i tuat ion. This example gives rise to an infinite family of non -abe l i an difference sets w i th pa rameters (4t 2, 2t a t, t 2 t), where t = 2 q. 3 r5 . 1 0 ' , q, r, s >/0, and r > 0 ~ q > 0. N o abel ian difference sets w i th th...
متن کاملOn central difference sets in certain non-abelian 2-groups
In this note, we define the class of finite groups of Suzuki type, which are non–abelian groups of exponent 4 and class 2 with special properties. A group G of Suzuki type with |G| = 22s always possesses a non–trivial difference set. We show that if s is odd, G possesses a central difference set, whereas if s is even, G has no non–trivial central difference set.
متن کاملDifference sets in non-abelian groups of order 256
This paper considers the problem of determining which of the 56092 groups of order 256 contain (256, 120, 56, 64) difference sets. John Dillon at the National Security Agency communicated 724 groups which were still open as of August 2012. In this paper, we present a construction method for groups containing a normal subgroup isomorphic to Z4 × Z4 × Z2. This construction method was able to prod...
متن کاملDifference sets in abelian 2-groups
If G is an abelian group of order u, and D is a subset of G with k elements such that every nonidentity element can be expressed 2 times in the form a b, where a and b are elements of D, then D is called a (u, k, A) difference set in G. The order n of the difference set is k 1. In this paper we consider the parameter values v = 22di 2, k = 22d+ ’ 24 ,I= 22d 2d, and n=22d. The rank r of G is the...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1993
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90226-j