منابع مشابه
Steiner Quadruple Systems with Point-regular Abelian Automorphism Groups
Abstract. In this paper we present a graph theoretic construction of Steiner quadruple systems (SQS) admitting abelian groups as point-regular automorphism groups. The resulting SQS has an extra property which we call A-reversibility, where A is the underlying abelian group. In particular, when A is a 2-group of exponent at most 4, it is shown that an A-reversible SQS always exists. When the Sy...
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Let t, v, k, λ be positive integers satisfying v > k > t. A t-(v, k, λ) design is an ordered pair (V,B), where V is a finite set of v points, B is a collection of k-subsets of V , say blocks, such that every t-subset of V occurs in exactly λ blocks in B. In what follows we simply write t-designs. A 3-(v, 4, 1) design is called a Steiner quadruple system and denoted by SQS(v). It is known that a...
متن کاملOn Quadruple Systems
( n — h\ 11 m — h\ I-hi I \l-hj is the number of those elements of S (I, m, n) which contain h fixed elements of E. It is known that condition (1) is not sufficient for S(l, m, n) to exist. It has been proved that no finite projective geometry exists with 7 points on every line. This implies non-existence of 5(2, 7, 43). There arises a problem of finding a necessary and sufficient condition for...
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A finite universal algebra is called strictly simple if it is simple and has no nontrivial subalgebras. An algebra is said to be Abelian if for every term t(x, ȳ) and for all elements a, b, c̄, d̄, we have the following implication: t(a, c̄) = t(a, d̄) −→ t(b, c̄) = t(b, d̄). It is shown that every finite simple Abelian universal algebra is strictly simple. This generalizes a well known fact about Ab...
متن کاملFinite Simple Abelian Algebras Are Strictly Simple
A finite universal algebra is called strictly simple if it is simple and has no nontrivial subalgebras. An algebra is said to be Abelian if for every term t(x,y) and for all elements a, b, c, d, we have the following implication: t(a,c) = t(a,d) —> t(b,c) = t(b,d) . It is shown that every finite simple Abelian universal algebra is strictly simple. This generalizes a well-known fact about Abelia...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2007
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2007.01.002