THE ORDER GRAPHS OF GROUPS
SH.
Payrovi
Imam Khomeini International University, Qazvin - IRAN.
author
H.
Pasebani
Imam Khomeini International University, Qazvin, IRAN.
author
text
article
2014
eng
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$G\cong C_{p^5}, C_3\times C_3$, $C_2\timesC_4$ or $G\cong Q_8$.
Algebraic Structures and Their Applications
Yazd University
2382-9761
1
v.
1
no.
2014
1
10
http://as.yazd.ac.ir/article_409_c5c1d4b6b27aef175b66fd0c85d2eac4.pdf
ENLARGED FUNDAMENTALLY VERY THIN Hv-STRUCTURES
T.
Vougiouklis
Democritus University of Thrace,
author
text
article
2014
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
1
v.
1
no.
2014
11
21
http://as.yazd.ac.ir/article_410_a84741ff38a501826228c29a144726fd.pdf
HYPERTRANSCENDENTAL FORMAL POWER SERIES OVER FIELDS OF POSITIVE CHARACTERISTIC
Habib
Sharif
Shiraz University
author
text
article
2014
eng
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 $f\in K((x))$ over $K$.Let $L$ be a field of characteristic zero. The power series $f\inL[[x]]$ 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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
1
v.
1
no.
2014
23
33
http://as.yazd.ac.ir/article_411_18804562d772712dfa86536f3e6ba671.pdf
STABILIZER TOPOLOGY OF HOOPS
R.A.
Borzooei
Shahid Beheshti University
author
M.
Aaly Kologani
Payamenour University, Tehran
author
text
article
2014
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
1
v.
1
no.
2014
35
48
http://as.yazd.ac.ir/article_412_2b7660c436537a35bbc015e90365dd28.pdf
AUTOMORPHISM GROUP OF GROUPS OF ORDER pqr
M.
Ghorbani
Shahid Rajaee Teacher Training University
author
F.
Nowroozi Larki
Shahid Rajaee Teacher Training University
author
text
article
2014
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
1
v.
1
no.
2014
49
56
http://as.yazd.ac.ir/article_413_d618acbaf2f7c98f8667ef4ce3c65ab7.pdf
COSPECTRALITY MEASURES OF GRAPHS WITH AT MOST SIX VERTICES
A.
Abdollahi
University of Isfahan
author
Sh.
Janbaz
University of Isfahan
author
M.R.
Oboudi
Shiraz University
author
text
article
2014
eng
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 $G$.
Algebraic Structures and Their Applications
Yazd University
2382-9761
1
v.
1
no.
2014
57
67
http://as.yazd.ac.ir/article_421_f8cdc6042860185defb4bc45c2b6542d.pdf