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Extending sloops of cardinality 16 to SQS-skeins with all possible congruence lattices
Authors: M. H. Armanious, E. M. A. Elzayat
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Abstract
It is well known that each STS(15) with a sub-STS(7) is derived [11]. In this article, we will improve this result by showing that each non-simple sloop L of cardinality 16 with any possible congruence lattice C(L) can be extended to a non-simple SQS-skein S of cardinality 16 with all possible congruence lattices for C(S). Accordingly, we may say that any triple system STS(15) with m sub-STS(7)s is a derived triple system from an SQS(16) having n sub-SQS(8)s for all possible non-zero numbers of m and n.M. H. Armanious,
E. M. A. Elzayat
Department of Mathematics,
Faculty of Science Revised May 17, 2004,
Mansoura University,
Mansoura,
Egypt.
E-mail:
E. M. A. Elzayat
Department of Mathematics,
Faculty of Science Revised May 17, 2004,
Mansoura University,
Mansoura,
Egypt.
E-mail:
Fulltext
– 0.30 Mb
Contents
- Extending sloops of cardinality 16 to SQS-skeins with all possible congruence lattices
- Weak implicative hyper BCK-ideals
- Necessary and sufficient conditions for the continuity of a pre-Haar system at a unit with singleton orbit
- The structure of extra loops
- Spurious multiplicative group of GF(pm): a new tool for cryptography
- Embedding of an AG**-groupoid in a commutative monoid
- Permutation representations of triangle group ?(2,4,5)
- Quotient hyper BCK-algebras
- Affine regular pentagons in GSquasigroups
