Related papers: A Construction of Metabelian Groups

Let p be an odd prime. The lattice of all normal subgroups and the terms of the lower and upper central series are determined for all metabelian p-groups with generator rank d=2 having abelianization of type (p,p) and minimal defect of…

We obtain a classification of the finite two-generated cyclic-by-abelian groups of prime-power order. For that we associate to each such group $G$ a list $\inv(G)$ of numerical group invariants which determines the isomorphism type of $G$.…

Let $p$ be a prime number and $\mathbb{Z}_p=\mathbb{Z}/p\mathbb{Z}$. We study finite groups with abelian derived subgroup and exponent $p$ in terms of group extension data and their matrix presentations. We show a one-to-one correspondence…

We use Constraint Satisfaction Methods to construct and enumerate finite $L$-algebras up to isomorphism. These objects were recently introduced by Rump and appear in Garside theory, algebraic logic, and the study of the combinatorial…

We characterize the finite groups of minimal order that admit an irreducible complex character of degree $p$ or $p^2$, where $p$ is a prime.

It is known that any locally graded group with finitely many derived subgroups of non-normal subgroups is finite-by-abelian. This result is generalized here, by proving that in a locally graded group $G$ the subgroup $\gamma_{k}(G)$ is…

We construct a family of finitely generated infinite periodic groups. The basic example is a 2-group, called the tetrahedron group. We generalize the construction by suggesting a family of infinite finitely generated dice groups. We provide…

Let G be any abelian group and {a_sG_s}_{s=1}^k be a finite system of cosets of subgroups G_1,...,G_k. We show that if {a_sG_s}_{s=1}^k covers all the elements of G at least m times with the coset a_tG_t irredundant then [G:G_t]\le 2^{k-m}…

There are several results in the literature concerning $p$-groups $G$ with a maximal elementary abelian normal subgroup of rank $k$ due to Thompson, Mann and others. Following an idea of Sambale we obtain bounds for the number of generators…

Let $G$ be a finite $p$-group of order $p^n$ and $M(G)$ be its Schur multiplier. It is well known result by Green that $|M(G)|= p^{\frac{1}{2}n(n-1)-t(G)}$ for some $t(G) \geq 0$. In this article we classify non-abelian $p$-groups $G$ of…

In 1963, Greenberg proved that every finite group appears as the monodromy group of some morphism of Riemann surfaces. In this paper, we give two constructive proofs of Greenberg's result. First, we utilize free groups, which given with the…

We give a complete classification of the 32-dimensional pointed Hopf algebras over an algebraically closed field k with characteristic different from 2. It turns out that there are infinite families of isomorphism classes of pointed Hopf…

We introduce a class of countable groups by some abstract group-theoretic conditions. It includes linear groups with finite amenable radical and finitely generated residually finite groups with some non-vanishing $\ell^2$-Betti numbers that…

If G and H are finitely generated, residually nilpotent metabelian groups, H is termed para-G if there is a homomorphism of G into H which induces an isomorphism between the corresponding terms of their lower central quotient groups. We…

The groups of order 64p without a normal sylow p-subgroup are listed, and their automorphism groups are also determined. As a by-product of our original effort to get these groups, we needed to determine the automorphism groups of those…

The results of computer computations determining the automorphism groups of the groups of order 32$p$ for $p \geq 3$ are given in several tables. Presentations for the automorphism groups of the groups of order 32, which in many cases…

It is shown that a finite group in which more than 3/4 of the elements are involutions must be an elementary abelian 2-group. A group in which exactly 3/4 of the elements are involutions is characterized as the direct product of the…

We generalise the constructions of Brady and Lodha to give infinite families of hyperbolic groups, each having a finitely presented subgroup that is not of type $F_3$. By calculating the Euler characteristic of the hyperbolic groups…

Let $G$ be a finite $p$-group of order $p^n$. It is known that $|\mathcal{M}(G)|=p^{\f{1}{2}n(n-1)-t(G)}$ and $t(G)\geq 0$. The structure of $G$ characterized when $t(G)\leq 4$ in \cite{be,el,ni,sa,zh}. The structure description of $G$ is…

If $G$ is a finite group and $k =q>2$ or $k=q+1$ for a prime power $q$ then, for infinitely many integers $v$, there is a $2$-$(v,k,1)$-design ${\bf D}$ for which ${\rm Aut} {\bf D}\cong G$.