Related papers: Construction of groups with triality and their cor…
Let $G$ be a simple algebraic group and $\ggg=\Lie(G)$ over $k=\bar\bbf_q$ where $q$ is a power of the prime characteristic of $k$, and $F$ a Frobenius morphism on $G$ which can be defined naturally on $\ggg$. In this paper, we investigate…
A group $G$ is said to be $\frac{3}{2}$-generated if every nontrivial element belongs to a generating pair. It is easy to see that if $G$ has this property then every proper quotient of $G$ is cyclic. In this paper we prove that the…
In this paper we study distortion of various well-known embeddings of finitely generated torsion-free nilpotent groups $G$ into unitriangular groups $UT_n(\mathbb{Z})$. We also provide a polynomial time algorithm for finding distortion of a…
In this paper, we will give the generic construction of a binary linear code of dimension $n+3$ and derive the necessary and sufficient conditions for the constructed code to be minimal. Using generic construction, a new family of minimal…
We study the intersection of finitely generated factor-free subgroups of free products of groups by utilizing the method of linear programming. For example, we prove that if $H_1$ is a finitely generated factor-free noncyclic subgroup of…
Let $S$ be either a free group or the fundamental group of a closed hyperbolic surface. We show that if $G$ is a finitely generated residually-$p$ group with the same pro-$p$ completion as $S$, then two-generated subgroups of $G$ are free.…
Consider any sequence of finite groups $A^t$, where $t$ takes values in an integer index set $\mathbf{Z}$. A group system $A$ is a set of sequences with components in $A^t$ that forms a group under componentwise addition in $A^t$, for each…
We study the (variable-length) codes of the form X u {a^n}, where X c a*wa* and |X| = n. We extend various notions and results from factorizations of cyclic groups theory to this type of codes. In particular, when n is the product of at…
We complete the building-up construction for self-dual codes by resolving the open cases over $GF(q)$ with $q \equiv 3 \pmod 4$, and over $\Z_{p^m}$ and Galois rings $\GR(p^m,r)$ with an odd prime $p$ satisfying $p \equiv 3 \pmod 4$ with…
For a positive integer n, let f(n) denote the smallest non-negative integer b such that for each system S \subseteq {x_k=1,x_i+x_j=x_k,x_i*x_j=x_k: i,j,k \in {1,...,n}} with a solution in non-negative integers x_1,...,x_n, there exists a…
Factors $\frac{X}{Y}$ in a free group $F$ with $Y$ normal in $X$ are considered. Precise results on the free structure of ${Y}$ relative to the free structure of ${X}$ when $\frac{X}{Y}$ is abelian are obtained. Some extensions and…
Let $G$ be a random torsion-free nilpotent group generated by two random words of length $\ell$ in $U_n(\mathbb{Z})$. Letting $\ell$ grow as a function of $n$, we analyze the step of $G$, which is bounded by the step of $U_n(\mathbb{Z})$.…
We propose and analyze a structure with which to organize the difference between a knot in the 3-sphere bounding a topologically embedded 2-disk in the 4-ball and it bounding a smoothly embedded disk. The n-solvable filtration of the…
In the present article we investigate the possibility of combining the usual Grassmann algebras with their ternary Z_3-graded counterpart, thus creating a more general algebra with coexisting quadratic and cubic constitutive relations. We…
We construct bundles $E_k(\A,\F) \to M$ over the complement $M$ of a complex hyperplane arrangement \A, depending on an integer $k \geq 1$ and a set $\F=\{f_1, \ldots, f_\mu\}$ of continuous functions $f_i \colon M \to \C$ whose differences…
Gray and Ruskuc have shown that any group G occurs as the maximal subgroup of some free idempotent generated semigroup IG(E) on a biordered set of idempotents E, thus resolving a long standing open question. Given the group G, they make a…
The space of invariants for a single matrix is generated by traces containing at most $N$ matrices per trace. We extend this analysis to multi-matrix models at finite $N$. Using the Molien-Weyl formula, we compute partition functions for…
We apply the free product construction to various local algebras in algebraic quantum field theory. If we take the free product of infinitely many identical half-sided modular inclusions with ergodic canonical endomorphism, we obtain a…
We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G and H are isomorphic. The n^(log n) barrier for group isomorphism has withstood all attacks --- even for the…
Grothendieck's theory of blended extensions (extensions panach\'ees) gives a natural framework to study 3-step filtrations in abelian categories. We give a generalization of this theory that is suitable for filtrations with an arbitrary…