Related papers: Subgroups of Division Rings
We determine the structure of the intersection of a finitely generated subgroup of a semiabelian variety $G$ defined over a finite field with a closed subvariety $X\subset G$.
We investigate the maximum length of a chain of subsemigroups in various classes of semigroups, such as the full transformation semigroups, the general linear semigroups, and the semigroups of order-preserving transformations of finite…
This article examines group ring codes over finite fields and finite groups. We also present a section on two-dimensional cyclic codes in the quotient ring $\mathbb{F}_q[x, y] / \langle x^{l} - 1, y^{m} - 1 \rangle$. These two-dimensional…
We describe an algorithm which determines whether or not a group which is hyperbolic relative to abelian groups admits a nontrivial splitting over a finite group.
We investigate properties of finite transitive permutation groups $(G, \Omega)$ in which all proper subgroups of $G$ act intransitively on $\Omega.$ In particular, we are interested in reduction theorems for minimally transitive…
We consider indecomposable representations of the Klein four group over a field of characteristic $2$ and of a cyclic group of order $pm$ with $p,m$ coprime over a field of characteristic $p$. For each representation we explicitly describe…
We study the distribution of principal ideals generated by irreducible elements in an algebraic number field.
A resolution of the intersection of a finite number of subgroups of an abelian group by means of their sums is constructed, provided the lattice generated by these subgroups is distributive. This is used for detecting singularities of…
Let G be a finite group and p a prime dividing its order. We define new collections of p-subgroups of G. We study the homotopy relations among them and with the standard collections of p-subgroups. We determine their ampleness and sharpness…
In this paper, cyclic codes are established over some finite quaternion integer rings with respect to the quaternion Mannheim distance, and de- coding algorithm for these codes is given.
Clifford algebras are used for constructing spin groups, and are therefore of particular importance in the theory of quantum mechanics. But the spin group is not the only subgroup of the Clifford algebra. An algebraist's perspective on…
Let $A$ be an Artin algebra. We investigate subalgebras of $A$ with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.
We give an overview on recent results concerning additive unit representations. Furthermore the solutions of some open questions are included. The central problem is whether and how certain rings are (additively) generated by their units.…
Let $F$ be a number field with ring of integers $\Oc_F$ and $\Dc$ a division $F$-algebra with a maximal cyclic subfield $K$. We study rings occurring as quotients of a natural $\Oc_F$-order $\Lambda$ in $\Dc$ by two-sided ideals. We reduce…
We explicate a number of notions of algebraic laminations existing in the literature, particularly in the context of an exact sequence $$1\to H\to G \to Q \to 1 $$ of hyperbolic groups. These laminations arise in different contexts:…
We study the special fibers of a certain class of absolutely simple abelian varieties over number fields with endomorphism rings $\bz$ and possessing $l$-adic monodromy groups of the least possible rank. We also study the Dirichlet density…
Given a field F, one may ask which finite groups are Galois groups of field extensions E/F such that E is a maximal subfield of a division algebra with center F. This question was originally posed by Schacher, who gave partial results over…
We investigate the superalgebra of derivations generated by the fundamental forms on manifolds with reduced structure group. In particular, we point out a relation between the algebra of derivations of heterotic geometries that admit…
We consider a convenient category of "quadratic" multirings, that allows simple functorial relations with categories associated with abstract quadratic forms theories and shares many good aspects of the theories of Special Groups and of…
The paper studies some properties of the ring of integer-valued quasi-polynomials. On this ring, theory of generalized Euclidean division and generalized GCD are presented. Applications to finite simple continued fraction expansion and…