We prove that the groups presented by finite convergent monadic rewriting systems with generators of finite order are exactly the free products of finitely many finite groups, thereby confirming Gilman’s Conjecture in a special case. We also prove that the finite cyclic groups of order at least three are the only finite groups admitting a presentation by more than one finite convergent monadic ...

The Artin exponent induced from cyclic subgroups of finite groups was studied extensively by T.Y. Lam in [5]. A Burnside ring theoretic version of the results in [5] for p-groups was given in [6]. Here we shall be interested in looking at the Artin exponent induced from the elementary abelian subgroups of finite p-groups using some results of A. Dress in [3].

Abstract The structure of locally soluble periodic groups in which every abelian subgroup is cyclic was described over 20 years ago. We complete the aforementioned characterization by dealing with non-periodic case. also describe finite all subgroups are cyclic.

We classify the permutation groups of cyclic codes over a finite field. As a special case, we find the permutation groups of non-primitive BCH codes of prime length. In addition, the Sylow p-subgroup of the permutation group is given for many cyclic codes of length p. Several examples are given to illustrate the results.

We give an algorithm for enumerating cosets of a group defined as a finite homomorphic image of a semi-direct product of free products of cyclic groups by a group of monomial automorphisms. Lots of finite groups, including some of the sporadic simple groups can be defined in this mannar. Mathematics Subject Classification: 20Bxx

a non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized fibonacci sequence , , , . a remarkable application of this definition may be find on the study of random covers in the cryptography. the 2-step generalized sequences for the dihedral groups studied for their pe...

Here we present a working framework to establish finite abelian groups in python. The primary aim is to allow new A-level students to work with examples of finite abelian groups using open source software. We include the code used in the implementation of the framework. We also prove some useful results regarding finite abelian groups which are used to establish the functions and help show how ...

How can we describe all finite groups? Before we address this question, let’s write down a list of all the finite groups of small orders ≤ 15, up to isomorphism. We have seen almost all of these already. If G is abelian, it is easy to write down all possible G of a given order, using the Fundamental Theorem of Finite Abelian Groups: G must be isomorphic to a direct product of cyclic groups, and...

We are interested in finite groups acting orientation-preservingly on 3–manifolds (arbitrary actions, ie not necessarily free actions). In particular we consider finite groups which contain an involution with nonempty connected fixed point set. This condition is satisfied by the isometry group of any hyperbolic cyclic branched covering of a strongly invertible knot as well as by the isometry gr...

The power graph of a group G is the graph whose vertex set is G and two distinct vertices are adjacent if one is a power of the other. In this paper, the minimum degree of power graphs of certain classes of cyclic groups, abelian p-groups, dihedral groups and dicyclic groups are obtained. It is ascertained that the edge-connectivity and minimum degree of power graphs are equal, and consequently...