The syntactic monoid of a hypercode.
The system of idempotents of a regular semigroup
The table of characters of some quasigroups
It is known that (ℤₙ,-ₙ) are examples of entropic quasigroups which are not groups. In this paper we describe the table of characters for quasigroups (ℤₙ,-ₙ).
The tame automorphism group of an affine quadric threefold acting on a square complex
We study the group of tame automorphisms of a smooth affine -dimensional quadric, which we can view as the underlying variety of . We construct a square complex on which the group admits a natural cocompact action, and we prove that the complex is and hyperbolic. We propose two applications of this construction: We show that any finite subgroup in is linearizable, and that satisfies the Tits alternative.
The tame degree and related invariants of non-unique factorizations
Local tameness and the finiteness of the catenary degree are two crucial finiteness conditions in the theory of non-unique factorizations in monoids and integral domains. In this note, we refine the notion of local tameness and relate the resulting invariants with the usual tame degree and the -invariant. Finally we present a simple monoid which fails to be locally tame and yet has nice factorization properties.
The tensor product and the 2nd nilpotent product of groups.
The tensor product of a semigroup with a union of groups.
The tensor product of exceptional representations on the general linear group
The tensor product of groupoids
The tensor product of right groups
The tensor product of semi-lattices.
The theorem of Borevich for the hyperbolic unitary group over a noncommutative field.
The theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry
In [Comput. Math. Appl. 41 (2001), 135--147], A. A. Ungar employs the Möbius gyrovector spaces for the introduction of the hyperbolic trigonometry. This Ungar's work plays a major role in translating some theorems from Euclidean geometry to corresponding theorems in hyperbolic geometry. In this paper we explore the theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry.
The theory of characters of commutative Hausdorff bicompact semigroups
The theory of dual groups
We study the -theory of sequences of dual groups and give a complete classification of the -elementary classes by finding simple invariants for them. We show that nonstandard models exist.
The theory of operations as the general theory of groups - Dissertation, Voronez, 1922, 80 pp. An historical review by L.M. Gluskin and B.M. Schein
The Tits alternative for . I: Dynamics of exponentially-growing automorphisms.
The Tits Group as a Standard Subgroup.
The Topological Version of Groups Generated by Reflections.
The topology of continuous partially-additive monoids