Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din Moldova"RO EN
Shortest single axioms with neutral element for groups of exponent 2 and 3
Authors: N. C. Fiala and K. M. Agre
– 0.21 Mb
Abstract
We study identities in product and a constant e only that are valid in all groups of exponent 2 (3) with neutral element e and that imply that a groupoid satisfying one of them is a group of exponent 2 (3) with neutral element e. Such an identity will be called a single axiom with neutral element for groups of exponent 2 (3). We utilize the automated reasoning software Prover9 and Mace4 to attempt to find all shortest single axioms with neutral element for groups of exponent 2 (3). Beginning with a list of 1323 (1716) candidate identities that contains all shortest possible single axioms with neutral element for groups of exponent 2 (3), we find 173 (148) single axioms with neutral element for groups of exponent (2) 3 and eliminate all but 5 (119) of the remaining identities as not being single axioms with neutral element for groups of exponent 3. We also prove that a finite model of any of these 5 (119) identities must be a group of exponent 2 (3) with neutral element e.Fulltext
– 0.21 Mb
Contents
- Bipolar fuzzy soft Lie algebras
- Soft intersection Lie algebras
- A study of n-subracks
- Weak hyper residuated lattices
- On classes of regularity in an ordered semigroup
- OD-Characterization of almost simple groups
- Zariski-topology for co-ideals of commutative semirings
- Shortest single axioms with neutral element for groups of exponent 2 and 3
- On 0-minimal (0,2)-bi-ideals
- Intra-regular, left quasi-regular and semisimple fuzzy ordered semigroups
- Nuclei and commutants of C-loops
- Simple ternary semigroups
