A Tribute to Mohammad Reza Darafsheh
Ali Reza
Ashrafi
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, I. R. Iran
author
Khadijeh
Fathalikhani
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, I. R. Iran
author
text
article
2018
eng
The decision to pay tribute to Mohammad Reza Darafsheh is for his major contributions to finite group theory in Iran and through scientific endeavor, publishing several papers in this topic and his action as an editor of a number of scientific journals.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
3
v.
2
no.
2018
75
79
http://mir.kashanu.ac.ir/article_88205_18143ed81980d0d5bfb4bdf84528f0de.pdf
dx.doi.org/10.22052/mir.2019.187293.1137
An Improved Hash Function Based on the Tillich-Zémor Hash Function
Ahmad
Gaeini
Department of Mathematics, Faculty of Science,
Imam Hossein Comprehensive University,
Tehran, I. R. Iran
author
Mohammad Hossein
Ghaffari
Department of Mathematics, Faculty of Science,
Imam Hossein Comprehensive University,
Tehran, I. R. Iran
author
Zohreh
Mostaghim
Cryptography and Data Security Laboratory, School of Mathematics,
Iran University of Science and Technology,
Tehran, I. R. Iran
author
text
article
2018
eng
Using the idea behind the Tillich-Zémor hash function, we propose a new hash function. Our hash function is parallelizable and its collision resistance is implied by a hardness assumption on a mathematical problem. Also, it is secure against the known attacks. It is the most secure variant of the Tillich-Zémor hash function until now.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
3
v.
2
no.
2018
81
87
http://mir.kashanu.ac.ir/article_64768_8e0dcee67425dfa7e0e5eb3b16640267.pdf
dx.doi.org/10.22052/mir.2018.97876.1078
A Simple Classification of Finite Groups of Order p2q2
Aziz
Seyyed Hadi
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University
author
Modjtaba
Ghorbani
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University
author
Farzaneh
Nowroozi Larki
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University
author
text
article
2018
eng
Suppose G is a group of order p^2q^2 where p>q are prime numbers and suppose P and Q are Sylow p-subgroups and Sylow q-subgroups of G, respectively. In this paper, we show that up to isomorphism, there are four groups of order p^2q^2 when Q and P are cyclic, three groups when Q is a cyclic and P is an elementary ablian group, p^2+3p/2+7 groups when Q is an elementary ablian group and P is a cyclic group and finally, p + 5 groups when both Q and P are elementary abelian groups.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
3
v.
2
no.
2018
89
98
http://mir.kashanu.ac.ir/article_45273_e39c942af529952ba55f29606887d4c6.pdf
dx.doi.org/10.22052/mir.2017.62726.1044
Some Structural Properties of Upper and Lower Central Series of Pairs of Groups
Azam
Kaheni
Ferdowsi University of Mashhad
author
Saeed
Kayvanfar
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
author
text
article
2018
eng
In this paper, we first present some properties of lower and upper central series of pair of groups. Then the notion of $n$-isoclinism for the classification of pairs of groups is introduced, and some of the structural properties of the created classes are proved. Moreover some interesting theorems such as Baer Theorem, Bioch Theorem, Hirsh Theorem for pair of groups are generalized. Finally, it is shown that each $n$-isoclinism family of pairs contains a quotient irreducible pair.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
3
v.
2
no.
2018
99
108
http://mir.kashanu.ac.ir/article_45109_b22684cd6fd03b64d74b22ff07832283.pdf
dx.doi.org/10.22052/mir.2017.56003.1035
Groups with Two Extreme Character Degrees and their Minimal Faithful Representations
Mahtab
Delfani
Department of Mathematics, Urmia University, Urmia, Iran
author
Houshang
Behravesh
Department of Mathematics, Urmia University, Urmia, Iran
author
text
article
2018
eng
for a finite group G, we denote by p(G) the minimal degree of faithful permutation representations of G, and denote by c(G), the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C. In this paper we will assume that, G is a p-group of exponent p and class 2, where p is prime and cd(G) = {1, |G : Z(G)|^1/2}. Then we will show that c(G)≤ |G : Z(G)|^{1/2} c(Z(G)) , p(G) ≤ |G : Z(G)|^{1/2}p(Z(G)):
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
3
v.
2
no.
2018
109
115
http://mir.kashanu.ac.ir/article_88262_bbea5fc48f8ecb778827001fced83bbd.pdf
dx.doi.org/10.22052/mir.2019.186347.1133
Fundamental Functor Based on Hypergroups and Groups
Mohammad
Hamidi
Department of Mathematics, Payame Noor University, Tehran, I. R. Iran
author
text
article
2018
eng
The purpose of this paper is to compute of fundamental relations of hypergroups. In this regards first we study some basic properties of fundamental relation of hypergroups, then we show that any given group is isomorphic to the fundamental group of a nontrivial hypergroup. Finally we study the connections between categories of hypergroups and groups via the fundamental relatio
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
3
v.
2
no.
2018
117
129
http://mir.kashanu.ac.ir/article_46681_5c960eb0fb46ee957fc0f50ee9fd2d21.pdf
dx.doi.org/10.22052/mir.2017.46681
On the Finite Groups that all Their Semi-Cayley Graphs are Quasi-Abelian
Majid
Arezoomand
University of Larestan
author
text
article
2018
eng
In this paper, we prove that every semi-Cayley graph over a group G is quasi-abelian if and only if G is abelian.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
3
v.
2
no.
2018
131
134
http://mir.kashanu.ac.ir/article_87320_869503634049640f029261cb68914de1.pdf
dx.doi.org/10.22052/mir.2019.127665.1101
On the Regular Power Graph on the Conjugacy Classes of Finite Groups
Sajjad
Mahmood Robati
Department of Mathematics, Faculty of science, Imam Khomeini international University
author
text
article
2018
eng
The (undirected) power graph on the conjugacy classes $\mathcal{P_C}(G)$ of a group $G$ is a simple graph in which the vertices are the conjugacy classes of $G$ and two distinct vertices $C$ and $C'$ are adjacent in $\mathcal{P_C}(G)$ if one is a subset of a power of the other. In this paper, we describe groups whose associated graphs are $k$-regular for $k=5,6$.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
3
v.
2
no.
2018
135
138
http://mir.kashanu.ac.ir/article_88414_ff1c56177711f42e8c43d4466df2e617.pdf
dx.doi.org/10.22052/mir.2019.172618.1118
Classification of Monogenic Ternary Semigroups
Nahid
Ashrafi
Faculty of Mathematics, Statistics and Computer Science
Semnan University
Semnan, Iran
author
Zahra
Yazdanmehr
Faculty of Mathematics, Statistics and Computer Science
Semnan University
Semnan, Iran
author
text
article
2018
eng
The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index and the same period are isomorphic. We also investigate structure of finite monogenic ternary semigroups and we prove that any finite monogenic ternary semigroup is isomorphic to a quotient ternary semigroup.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
3
v.
2
no.
2018
139
146
http://mir.kashanu.ac.ir/article_88436_9d35edfa9b15675083a1676c24fd7b68.pdf
dx.doi.org/10.22052/mir.2019.173544.1120
1-Designs from the group $PSL_{2}(59)$ and their automorphism groups
Reza
Kahkeshani
University of Kashan
author
text
article
2018
eng
In this paper, we consider the projective special linear group $PSL_2(59)$ and construct some 1-designs by applying the Key-Moori method on $PSL_2(59)$. Moreover, we obtain parameters of these designs and their automorphism groups. It is shown that $PSL_2(59)$ and $PSL_2(59):2$ appear as the automorphism group of the constructed designs.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
3
v.
2
no.
2018
147
158
http://mir.kashanu.ac.ir/article_88470_659870553713da42a799e50be9b8af81.pdf
dx.doi.org/10.22052/mir.2017.68740.1048
(c,1,...,1) Polynilpotent Multiplier of some Nilpotent Products of Groups
Azam
Kaheni
Department of Mathematics, University of Birjand,
Birjand 615-97175, I. R. Iran
author
Saeed
Kayvanfar
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
author
text
article
2018
eng
In this paper we determine the structure of (c,1,...,1) polynilpotent multiplier of certain class of groups. The method is based on the characterizing an explicit structure for the Baer invariant of a free nilpotent group with respect to the variety of polynilpotent groups of class row (c,1,...,1).
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
3
v.
2
no.
2018
159
171
http://mir.kashanu.ac.ir/article_89271_6011d9b20decc8781cd94b0c49778d84.pdf
dx.doi.org/10.22052/mir.2019.190182.1150