Termal groupoids
We investigate the factor of the groupoid of terms through the largest congruence with a given set among its blocks. The set is supposed to be closed for overterms.
Terms and semiterms
Ternary halfgroupoids and coordinatization
Ternary halfgroupoids and coordinatization (Preliminary communication)
Ternary quasigroups and the modular group
For a positive integer , the usual definitions of -quasigroups are rather complicated: either by combinatorial conditions that effectively amount to Latin -cubes, or by identities on different -ary operations. In this paper, a more symmetrical approach to the specification of -quasigroups is considered. In particular, ternary quasigroups arise from actions of the modular group.
Ternary rings associated to translation plane
Ternary semigroups of morphisms of objects in categories
In this paper the notion of a ternary semigroup of morphisms of objects in a category is introduced. The connection between an isomorphism of categories and an isomorphism of ternary semigroups of morphisms of suitable objects in these categories is considered. Finally, the results obtained for general categories are applied to the categories and which were studied in [5].
Ternary spaces, media, and Chebyshev sets
Ternary structures and groupoids
Ternary structures and partial semigroups
Test elements and test rank of a free metabelian group.
Test elements and the retract theorem in hyperbolic groups.
Testing Cayley graph densities
We present a computer-assisted analysis of combinatorial properties of the Cayley graphs of certain finitely generated groups: given a group with a finite set of generators, we study the density of the corresponding Cayley graph, that is, the least upper bound for the average vertex degree (= number of adjacent edges) of any finite subgraph. It is known that an -generated group is amenable if and only if the density of the corresponding Cayley graph equals to . We test amenable and non-amenable...
Tetravalent Arc-Transitive Graphs of Order 3p 2
Let s be a positive integer. A graph is s-transitive if its automorphism group is transitive on s-arcs but not on (s + 1)-arcs. Let p be a prime. In this article a complete classification of tetravalent s-transitive graphs of order 3p2 is given
Tetravalent half-arc-transitive graphs of order
We classify tetravalent -half-arc-transitive graphs of order , where and , are distinct odd primes. This result involves a subclass of tetravalent half-arc-transitive graphs of cube-free order.
Tetravalent non-normal Cayley graphs of order .
The 1-Cohomology of the Adjoint Module of a Chevalley Group.
The 27-dimensional module for E6. I.
The 3-modular characters of the twisted Chevalley group 2D4(2) y 2D4(2).2.
In this paper we calculate the 3-modular character table of the twisted Chevalley group 2D4(2) and its automorphism group 2D4(2).2. The Meat-Axe package for calculating modular characters over finite fields (Ryba (1990)) was used to calculate most of the characters. The method of condensation, which was explained in Suleiman (1990) was used to determine the complete character table. All these methods are explained later in this paper.
The 4-string braid group has property RD and exponential mesoscopic rank
We prove that the braid group on 4 strings, its central quotient , and the automorphism group of the free group on 2 generators, have the property RD of Haagerup–Jolissaint. We also prove that the braid group is a group of intermediate mesoscopic rank (of dimension 3). More precisely, we show that the above three groups have exponential mesoscopic rank, i.e., that they contain exponentially many large flat balls which are not included in flats.