Aküzüm, Yesim Deveci, Ömür
Published in
Topological Algebra and its Applications

In [5], Deveci defined the Jacobsthal-Padovan p-sequence. In this paper,we extend this sequence to groups. Then we define the Jacobsthal-Padovan p-orbit and we study the Jacobsthal-Padovan p-orbits of the finite groups in detail. Furthermore, we obtain the lengths of the periods of the Jacobsthal-Padovan p-orbits of the Fox groups G1,l for l ≥ 3 as...

Fujii, Michihiko Satoh, Takao

We consider the pure Artin group of dihedral type, which is the kernel of the natural projection from the Artin group of dihedral type I2(k) to the associated Coxeter group. We present a rational function expression for the geodesic growth series of the pure Artin group of dihedral type with respect to a natural generating set, and we explicitly de...

Klyachko, Anton A. Mkrtchyan, Anna A.

We prove a general divisibility theorem that implies, e.g., that, in any group, the number of generating pairs (as well as triples, etc.) is a multiple of the order of the commutator subgroup. Another corollary says that, in any associative ring, the number of Pythagorean triples (as well as four-tuples, etc.) of invertible elements is a multiple o...

Adian, S. I. Atabekyan, V. S.
Published in
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)

In this paper we provide an overview of the results relating to the n-periodic products of groups that have been obtained in recent years by the authors of the present paper, as well as some results obtained by other authors in this direction. The periodic products were introduced by S.I. Adian in 1976 to solve the Maltsev’s well-known problem. It ...

Deveci, Omur Taş, Sait Kılıçman, A
Published in
Advances in Difference Equations

In this paper, we define the 2k-step Jordan-Fibonacci sequence, and then we study the 2k-step Jordan-Fibonacci sequence modulo m. Also, we obtain the cyclic groups from the multiplicative orders of the generating matrix of the 2k-step Jordan-Fibonacci sequence when read modulo m, and we give the relationships among the orders of the cyclic groups o...

Eick, Bettina Engel, Ann-Kristin
Published in
Groups Complexity Cryptology

We consider the isomorphism problem for the finitely generated torsion free nilpotent groups of Hirsch length at most five. We show how this problem translates to solving an explicitly given set of polynomial equations. Based on this, we introduce a canonical form for each isomorphism type of finitely generated torsion free nilpotent group of Hirsc...

Guyot, Luc

Let R be a unital commutative ring and let $M$ be an $R$-module that is generated by $k$ elements but not less. Let $E_n(R)$ be the subgroup of $GL_n(R)$ generated by the elementary matrices. In this paper we study the action of $E_n(R)$ by matrix multiplication on the set $Um_n(M)$ of unimodular rows of $M$ of length $n \ge k$. Assuming $R$ is mor...

Macedońska, Olga
Published in
Open Mathematics

The group of fractions of a semigroup S, if exists, can be written as G = SS−1. If S is abelian, then G must be abelian. We say that a semigroup identity is transferable if being satisfied in S it must be satisfied in G = SS−1. One of problems posed by G.Bergman in 1981 asks whether the group G must satisfy every semigroup identity which is satisfi...

Fernandes, Maria Elisa Leemans, Dimitri Weiss, Asia Ivić
Published in
Aequationes mathematicae

We study incidence geometries that are thin and residually connected. These geometries generalise abstract polytopes. In this generalised setting, guided by the ideas from the polytope theory, we introduce the concept of chirality, a property of orderly asymmetry occurring frequently in nature as a natural phenomenon. The main result in this paper ...

Farrokhi, M.D.G. Mohammadian, A.

We give the classification of all (minimal) Cayley bipartite or perfect finite groups as well as finite graphs $Gamma$ for which there are only finitely many (minimal) Cayley $Gamma$-free groups.