Yazd University
Algebraic Structures and Their Applications
2382-9761
1
1
2014
02
01
THE ORDER GRAPHS OF GROUPS
1
10
EN
SH.
Payrovi
Imam Khomeini International University, Qazvin - IRAN.
H.
Pasebani
Imam Khomeini International University, Qazvin, IRAN.
Let $G$ be a group. The order graph of $G$ is the (undirected)graph $Gamma(G)$,those whose vertices are non-trivial subgroups of $G$ and two distinctvertices $H$ and $K$ are adjacent if and only if either$o(H)|o(K)$ or $o(K)|o(H)$. In this paper, we investigate theinterplay between the group-theoretic properties of $G$ and thegraph-theoretic properties of $Gamma(G)$. For a finite group$G$, we show that $Gamma(G)$ is a connected graph with diameter at mosttwo, and $Gamma(G)$ is a complete graph ifand only if $G$ is a $p$-group for some prime number $p$. Furthermore,it is shown that $Gamma(G)=K_5$ if and only if either$Gcong C_{p^5}, C_3times C_3$, $C_2timesC_4$ or $Gcong Q_8$.
Finite group,Connected graph,star graph
http://as.yazd.ac.ir/article_409.html
http://as.yazd.ac.ir/article_409_c5c1d4b6b27aef175b66fd0c85d2eac4.pdf
Yazd University
Algebraic Structures and Their Applications
2382-9761
1
1
2014
02
01
ENLARGED FUNDAMENTALLY VERY THIN Hv-STRUCTURES
11
21
EN
T.
Vougiouklis
Democritus University of Thrace,
We study a new class of $H_v$-structures called Fundamentally Very Thin. This is an extension of the well known class of the Very Thin hyperstructures. We present applications of these hyperstructures.
Hyperstructures,$H_{v}$-structures,hopes,$\partial$-hopes
http://as.yazd.ac.ir/article_410.html
http://as.yazd.ac.ir/article_410_a84741ff38a501826228c29a144726fd.pdf
Yazd University
Algebraic Structures and Their Applications
2382-9761
1
1
2014
02
01
HYPERTRANSCENDENTAL FORMAL POWER SERIES OVER FIELDS OF POSITIVE CHARACTERISTIC
23
33
EN
Habib
Sharif
Shiraz University
sharif@susc.ac.ir
Let $K$ be a field of characteristic$p>0$, $K[[x]]$, the ring of formal power series over $ K$,$K((x))$, the quotient field of $ K[[x]]$, and $ K(x)$ the fieldof rational functions over $K$. We shall give somecharacterizations of an algebraic function $fin K((x))$ over $K$.Let $L$ be a field of characteristic zero. The power series $finL[[x]]$ is called differentially algebraic, if it satisfies adifferential equation of the form $P(x, y, y',...)=0$, where $P$is a non-trivial polynomial. This notion is defined over fields ofcharacteristic zero and is not so significant over fields ofcharacteristic $p>0$, since $f^{(p)}=0$. We shall define ananalogue of the concept of a differentially algebraic power seriesover $K$ and we shall find some more related results.
Formal Power Series,Algebraic Formal Power Series,Differentially Algebraic Formal Power Series
http://as.yazd.ac.ir/article_411.html
http://as.yazd.ac.ir/article_411_18804562d772712dfa86536f3e6ba671.pdf
Yazd University
Algebraic Structures and Their Applications
2382-9761
1
1
2014
02
01
STABILIZER TOPOLOGY OF HOOPS
35
48
EN
R.A.
Borzooei
Shahid Beheshti University
M.
Aaly Kologani
Payamenour University, Tehran
In this paper, we introduce the concepts of right, left and product stabilizers on hoops and study some properties and the relation between them. And we try to find that how they can be equal and investigate that under what condition they can be filter, implicative filter, fantastic and positive implicative filter. Also, we prove that right and product stabilizers are filters and if they are proper, then they are prime filters. Then by using the right stabilizers produce a basis for a topology on hoops. We show that the generated topology by this basis is Baire, connected, locally connected and separable and we investigate the other properties of this topology. Also, by the similar way, we introduce the right, left and product stabilizers on quotient hoops and introduce the quotient topology that is generated by them and investigate that under what condition this topology is Hausdorff space, $T_{0}$ or $T_{1}$ spaces.
Hoop algebra,stabilizer topology,Baire space,connected,locally connected,separable topology
http://as.yazd.ac.ir/article_412.html
http://as.yazd.ac.ir/article_412_2b7660c436537a35bbc015e90365dd28.pdf
Yazd University
Algebraic Structures and Their Applications
2382-9761
1
1
2014
02
01
AUTOMORPHISM GROUP OF GROUPS OF ORDER pqr
49
56
EN
M.
Ghorbani
Shahid Rajaee Teacher Training University
F.
Nowroozi Larki
Shahid Rajaee Teacher Training University
H"{o}lder in 1893 characterized all groups of order $pqr$ where $p>q>r$ are prime numbers. In this paper, by using new presentations of these groups, we compute their full automorphism group.
Affine group,Frobenius group,Automorphism group
http://as.yazd.ac.ir/article_413.html
http://as.yazd.ac.ir/article_413_d618acbaf2f7c98f8667ef4ce3c65ab7.pdf
Yazd University
Algebraic Structures and Their Applications
2382-9761
1
1
2014
02
01
COSPECTRALITY MEASURES OF GRAPHS WITH AT MOST SIX VERTICES
57
67
EN
A.
Abdollahi
University of Isfahan
Sh.
Janbaz
University of Isfahan
M.R.
Oboudi
Shiraz University
Cospectrality of two graphs measures the differences between the ordered spectrum of these graphs in various ways. Actually, the origin of this concept came back to Richard Brualdi's problems that are proposed in cite{braldi}: Let $G_n$ and $G'_n$ be two nonisomorphic simple graphs on $n$ vertices with spectra$$lambda_1 geq lambda_2 geq cdots geq lambda_n ;;;text{and};;; lambda'_1 geq lambda'_2 geq cdots geq lambda'_n,$$ respectively. Define the distance between the spectra of $G_n$ and $G'_n$ as$$lambda(G_n,G'_n) =sum_{i=1}^n (lambda_i-lambda'_i)^2 ;;; big(text{or use}; sum_{i=1}^n|lambda_i-lambda'_i|big).$$Define the cospectrality of $G_n$ by$text{cs}(G_n) = min{lambda(G_n,G'_n) ;:; G'_n ;;text{not isomorphic to} ; G_n}.$Let $text{cs}_n = max{text{cs}(G_n) ;:; G_n ;;text{a graph on}; n ;text{vertices}}.$Investigation of $text{cs}(G_n)$ for special classes of graphs and finding a good upper bound on $text{cs}_n$ are two main questions in thissubject.In this paper, we briefly give some important results in this direction and then we collect all cospectrality measures of graphs with at most six vertices with respect to three norms. Also, we give the shape of all graphs that are closest (with respect to cospectrality measure) to a given graph $G$.
Spectra of graphs,edge deletion,adjacency matrix of a graph
http://as.yazd.ac.ir/article_421.html
http://as.yazd.ac.ir/article_421_f8cdc6042860185defb4bc45c2b6542d.pdf