Difference sets in Abelian groups
نویسندگان
چکیده
منابع مشابه
Difference 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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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...
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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.
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A McFarland difference set is a difference set with parameters (v,k, 2 )= (qd+l(qd+qa-l+...+q+2),qa(qd+qa l + . . . + q + l ) , qd(qa-l+qa-2+...+ q + 1)), where q=p/and p is a prime. Examples for such difference sets can be obtained in all groups of G which contain a subgroup E ~-EA(q a+ 1) such that the hyperplanes of E are normal subgroups of G. In this paper we study the structure of the Syl...
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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...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1960
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1960-0117169-3