On Semi-Symmetric Quasigroups. (Short Communication).
On Solving A System Of Balanced Functional Equations Of Quaigroups III
On solving a system of balanced functional equations on quasigroups III.
On Solving A System Of Balanced Functional Equations On Quasigroups II
On Steiner loops and power associativity.
On Steiner manifolds
On Steiner quasigroups
On subdirectly irreducible Steiner loops of cardinality .
On the dimensions of automorphism groups of four-dimensional double loops.
On the existence of a Haar measure in topological IP-loops
In this paper, we give conditions ensuring the existence of a Haar measure in topological IP-loops.
On the multiplicative structure of finite division rings.
On the resolvability of Hall triple systems
È ben noto che fra le classi di sistemi ternari di Hall (HTS), gli HTS Abeliani ammettano una risoluzione siccome sono esattamente gli spazi affini finiti d'ordine 3; per questi sistemi una tal risoluzione è fornita dalla relazione di parallelismo. In questa nota viene dimostrato che certe classi di HTS non Abeliani costrutti dai gruppi di Burnside , anche ammettono una risoluzione. Allora, questi esempi di HTS si possono considerare anche come spazi finiti di Sperner e dunque la nota conclude...
On the semigroup structure of cyclic left distributive algebras.
On the solvability of commutative loops and their multiplication groups
We investigate the situation when the inner mapping group of a commutative loop is of order , where is a prime number, and we show that then the loop is solvable.
On the Specht property of varieties of commutative alternative algebras over a field of characteristic 3 and commutative Moufang loops.
On the structure and zero divisors of the Cayley-Dickson sedenion algebra
The algebras ℂ (complex numbers), ℍ (quaternions), and 𝕆 (octonions) are real division algebras obtained from the real numbers ℝ by a doubling procedure called the Cayley-Dickson Process. By doubling ℝ (dim 1), we obtain ℂ (dim 2), then ℂ produces ℍ (dim 4), and ℍ yields 𝕆 (dim 8). The next doubling process applied to 𝕆 then yields an algebra 𝕊 (dim 16) called the sedenions. This study deals with the subalgebra structure of the sedenion algebra 𝕊 and its zero divisors. In particular, it shows...
On the structure of finite loop capable Abelian groups
Loop capable groups are groups which are isomorphic to inner mapping groups of loops. In this paper we show that abelian groups , where and is an odd prime, are not loop capable groups. We also discuss generalizations of this result.
On the structure of finite loop capable nilpotent groups
In this paper we consider finite loops and discuss the problem which nilpotent groups are isomorphic to the inner mapping group of a loop. We recall some earlier results and by using connected transversals we transform the problem into a group theoretical one. We will get some new answers as we show that a nilpotent group having either , as the Sylow -subgroup for some odd prime or the group of quaternions as the Sylow -subgroup may not be loop capable.
On the structure of finite paramedial quasigroups
Information on the structure of finite paramedial quasigroups, including a classification of finite simple paramedial quasigroups, is given. The problem ``Classify the finite simple paramedial quasigroups'' was posed by J. Ježek and T. Kepka at the conference LOOPS'03, Prague 2003.
On the uniqueness of loops
Let be a finite group and the cyclic group of order 2. Consider the 8 multiplicative operations , where . Define a new multiplication on by assigning one of the above 8 multiplications to each quarter , for . If the resulting quasigroup is a Bol loop, it is Moufang. When is nonabelian then exactly four assignments yield Moufang loops that are not associative; all (anti)isomorphic, known as loops .