The Obstruction theory of Group Extensions and H^3(Q, A) in Abstract Categories
The one-block property in varieties of semigroups.
The operation in operator algebras
The binary operation , called Jordan triple product, and its variants (such as e.g. the sequential product or the inverted Jordan triple product ) appear in several branches of operator theory and matrix analysis. In this paper we briefly survey some analytic and algebraic properties of these operations, and investigate their intimate connection to Thompson type isometries in different operator algebras.
The orbits of the Hurwitz action of the braid groups on the standard generators
The Hurwitz action of the n-braid group Bₙ on the n-fold direct product of the m-braid group is studied. We show that the orbit of any n- tuple of the n standard generators of consists of the (n-1)th powers of n+1 elements.
The order dimension of Bruhat order on infinite Coxeter groups.
The order of a finite Coxeter group.
The order of normalform hypersubstitutions of type (2)
In [2] it was proved that all hypersubstitutions of type τ = (2) which are not idempotent and are different from the hypersubstitution whichmaps the binary operation symbol f to the binary term f(y,x) haveinfinite order. In this paper we consider the order of hypersubstitutionswithin given varieties of semigroups. For the theory of hypersubstitution see [3].
The orderability of idempotent semigroups
The orderability of regular semigroups.
The Ore conjecture
The Ore conjecture, posed in 1951, states that every element of every finite non-abelian simple group is a commutator. Despite considerable effort, it remains open for various infinite families of simple groups. In this paper we develop new strategies, combining character-theoretic methods with other ingredients, and use them to establish the conjecture.
The other -theorem
The -central extension of the Mapping Class Group of orientable surfaces
Topological Quantum Field Theories are closely related to representations of Mapping Class Groups of surfaces. Considering the case of the TQFTs derived from the Kauffman bracket, we describe the central extension coming from this representation, which is just a projective extension.
The -nilpotency of finite groups with some weakly pronormal subgroups
For a finite group and a fixed Sylow -subgroup of , Ballester-Bolinches and Guo proved in 2000 that is -nilpotent if every element of with order lies in the center of and when , either every element of with order lies in the center of or is quaternion-free and is -nilpotent. Asaad introduced weakly pronormal subgroup of in 2014 and proved that is -nilpotent if every element of with order is weakly pronormal in and when , every element of with order is also...
The -injectors of a finite group
The p-adic Topology on a Free Group: A Counterexample.
The parametrization of interior algebras.
The partial groupoid of idempotents of a regular semigroup.
The partially ordered collection of regular ...-classes of S(X).
The partially ordered family of C M-homomorphisms.
The partially ordered set of all J-classes of a finite semigroup.