‎Let $G$ be a finite group which is not a cyclic $p$-group‎, ‎$p$ a prime number‎. ‎We define an undirected simple graph $Delta(G)$ whose‎ ‎vertices are the proper subgroups of $G$, which are not contained in the‎ ‎Frattini subgroup of $G$ and two vertices $H$ and $K$ are joined by an edge‎ ‎if and only if $G=langle H‎ , ‎Krangle$‎. ‎In this paper we classify finite groups with planar graph‎. ‎...

a finite group g is said to be a pos-group if for each x in g the cardinality of the set {y in g | o(y) = o(x)} is a divisor of the order of g. in this paper we study the structure of pos-groups with some cyclic sylow subgroups.

a finite group g is said to be a pos-group if for each x in g the cardinality of the set {y in g | o(y) = o(x)} is a divisor of the order of g. in this paper we study the structure of pos-groups with some cyclic sylow subgroups.

We give the class of finite groups which arise as the permutation groups of cyclic codes over finite fields. Furthermore, we extend the results of Brand and Huffman et al. and we find the properties of the set of permutations by which two cyclic codes of length p can be equivalent. We also find the set of permutations by which two quasi-cyclic codes can be equivalent.

In this paper we formalized some theorems concerning the cyclic groups of prime power order. We formalize that every commutative cyclic group of prime power order is isomorphic to a direct product of family of cyclic groups [1], [18]. Let G be a finite group. The functor Ordset(G) yielding a subset of N is defined by the term (Def. 1) the set of all ord(a) where a is an element of G. One can ch...

We give a simple proof of the finite presentation of Sela's limit groups by using free actions on R n-trees. We first prove that Sela's limit groups do have a free action on an R n-tree. We then prove that a finitely generated group having a free action on an R n-tree can be obtained from free abelian groups and surface groups by a finite sequence of free products and amalgamations over cyclic ...

We give a simple proof of the finite presentation of Sela's limit groups by using free actions on R n-trees. We first prove that Sela's limit groups do have a free action on an R n-tree. We then prove that a finitely generated group having a free action on an R n-tree can be obtained from free abelian groups and surface groups by a finite sequence of free products and amalgamations over cyclic ...

We give a simple proof of the finite presentation of Sela’s limit groups by using free actions on Rn–trees. We first prove that Sela’s limit groups do have a free action on an Rn–tree. We then prove that a finitely generated group having a free action on an Rn–tree can be obtained from free abelian groups and surface groups by a finite sequence of free products and amalgamations over cyclic gro...

Recall that a group is called semiabelian if it is generated by its normal cyclic subgroups [6]. The class of semiabelian groups is a very natural generalization of the wellknown class of Dedekind groups (the groups in which all cyclic subgroups are normal). In the paper [6] Venzke showed that these groups could play a major role in the theory of supersoluble finite groups. Based on the notion ...

This article continues a prior investigation of the authors with the goal of extending characterization results of convolutional tight frames from the context of cyclic groups to general finite abelian groups. The collections studied are formed by translating a number of generators by elements of a fixed subgroup and it is shown, under certain norm conditions, that tight frames with this struct...