Related papers: Egyptian fractions on groups
We study group extensions of Finite Abelian Groups using matrices. We also prove a Theorem for equivalence of extensions using matrices.
We survey some results on the structure of the groups which are definable in theories of fields involved in the applications of model theory to Diophantine geometry. We focus more particularly on separably closed fields of finite degree of…
Hopf algebra structures on the extended q-superplane and its differential algebra are defined. An algebra of forms which are obtained from the generators of the extended q-superplane is introduced and its Hopf algebra structure is given
We will discuss about a possible method of using the cubit rod by the architects and the surveyors of Ancient Egypt to measure and draw lengths, comparing it with the other interpretations present in Literature. Instead of the modern…
We consider a toy model of a 3-dimensional topological quantum gravity. In this model, a contribution of a given 3-manifold is given by the partition function of an abelian Topological Quantum Field Theory (TQFT), with a topological…
We study certain subgroups of the full group of Hopf algebra automorphisms of a biproduct. In the process interesting subgroups of certain permutation groups come into play.
We describe methods to determine all the possible torsion groups of an elliptic curve that actually appear over a fixed quadratic field. We use these methods to find, for each group that can appear over a quadratic field, the field with the…
We define a metric ultraproduct of topological groups with left-invariant metric, and show that there is a countable sequence of finite groups with left-invariant metric whose metric ultraproduct contains isometrically as a subgroup every…
We define a partition of a reductive group into finitely many subsets, refining the partition of the group into strata. We state some conjectural properties of these subsets (called substrata) and verify them in some examples.
We show that reasonably well behaved 3d and 4D TQFts must contain certain algebraic structures. In 4D, we find both Hopf categories and trialgebras.
We give an explicit description of the category of central extensions of a group scheme by a sheaf of Abelian groups. Based on this, we describe a framework for computing with central extensions of finite commutative group schemes, torsors…
We study topological group theoretic properties of algebraic groups over local fields. In particular, we find conditions under which such groups have closed images under arbitrary continuous homomorphisms into arbitrary topological groups.
In general the endomorphisms of a non-abelian group do not form a ring under the operations of addition and composition of functions. Several papers have dealt with the ring of functions defined on a group which are endomorphisms when…
This is a survey on appearances of reflection groups, real and complex, in algebraic geometry. We also include a brief introduction into the theory of reflection groups.
Even though flt is a number theoretic result we prove that the result depends on the topological as well as the field structure of the underlying space.
We classify, up to isomorphism and up to equivalence, division gradings (by abelian groups) on finite-dimensional simple real algebras. Gradings on finite-dimensional simple algebras are determined by division gradings, so our results give…
We make a list of finite simple groups whose group rings over a given field are serial.
In this work we have considered the complexity of the different structures as topological group on Z. We collect some new results, as well as some known results on the group of the integers in order to present: -A family of $2^\cont$…
In this paper, we study residues of differential 2-forms on a smooth algebraic surface over an arbitrary field and give several statements about sums of residues. Afterwards, using these results we construct algebraic-geometric codes which…
Recently, sub-indices and sub-factors of groups with connections to number theory, additive combinatorics, and factorization of groups have been introduced and studied. Since all group subsets are considered in the theory and there are many…