University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
3
2
2018
12
01
An Improved Hash Function Based on the Tillich-Zémor Hash Function
81
87
EN
Ahmad
Gaeini
Department of Mathematics, Faculty of Science,
Imam Hossein Comprehensive University,
Tehran, I. R. Iran
againi@ihu.ac.ir
Mohammad Hossein
Ghaffari
Department of Mathematics, Faculty of Science,
Imam Hossein Comprehensive University,
Tehran, I. R. Iran
mhghaffari@alumni.iust.ac.ir
Zohreh
Mostaghim
Cryptography and Data Security Laboratory, School of Mathematics,
Iran University of Science and Technology,
Tehran, I. R. Iran
mostaghim@iust.ac.ir
10.22052/mir.2018.97876.1078
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.
The Tillich-Zemor hash function,Cayley hash function,special linear group
https://mir.kashanu.ac.ir/article_64768.html
https://mir.kashanu.ac.ir/article_64768_8e0dcee67425dfa7e0e5eb3b16640267.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
3
2
2018
12
01
A Simple Classification of Finite Groups of Order p2q2
89
98
EN
Aziz
Seyyed Hadi
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University
aziz.saidhadi@gmail.com
Modjtaba
Ghorbani
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University
mghorbani@srttu.edu
Farzaneh
Nowroozi Larki
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University
fnowroozi@gmail.com
10.22052/mir.2017.62726.1044
Suppose G is a group of order p<sup>2</sup>q<sup>2</sup> 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<sup>2</sup>q<sup>2</sup> when Q and P are cyclic, three groups when Q is a cyclic and P is an elementary ablian group, p<sup>2</sup>+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.
Semi-direct product,p-group,Sylow subgroup
https://mir.kashanu.ac.ir/article_45273.html
https://mir.kashanu.ac.ir/article_45273_e39c942af529952ba55f29606887d4c6.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
3
2
2018
12
01
Some Structural Properties of Upper and Lower Central Series of Pairs of Groups
99
108
EN
Azam
Kaheni
Department of Pure Mathematics,
Ferdowsi University of Mashhad,
Mashhad, Iran
azamkaheni@yahoo.com
Saeed
Kayvanfar
Department of Pure Mathematics,
Ferdowsi University of Mashhad,
Mashhad, Iran
skayvanf@um.ac.ir
10.22052/mir.2017.56003.1035
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.
n-Isoclinism,pair of groups,Quotient irreducible pair,pi-groups
https://mir.kashanu.ac.ir/article_45109.html
https://mir.kashanu.ac.ir/article_45109_b22684cd6fd03b64d74b22ff07832283.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
3
2
2018
12
01
Groups with Two Extreme Character Degrees and their Minimal Faithful Representations
109
115
EN
Mahtab
Delfani
Department of Mathematics, Urmia University, Urmia, Iran
ma.delfani@gmail.com
Houshang
Behravesh
Department of Mathematics, Urmia University, Urmia, Iran
h.behravesh@gmail.com
10.22052/mir.2019.186347.1133
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)|<sup>1/2</sup>}. Then we will show that c(G)≤ |G : Z(G)|<sup>1/2</sup> c(Z(G)) , p(G) ≤ |G : Z(G)|<sup>1/2</sup>p(Z(G)):
quasi-permutation,Linear character,Non-linear character
https://mir.kashanu.ac.ir/article_88262.html
https://mir.kashanu.ac.ir/article_88262_bbea5fc48f8ecb778827001fced83bbd.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
3
2
2018
12
01
Fundamental Functor Based on Hypergroups and Groups
117
129
EN
Mohammad
Hamidi
Department of Mathematics, Payame Noor University, Tehran, I. R. Iran
m.hamidi@pnu.ac.ir
10.22052/mir.2017.46681
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<br />fundamental relatio
Group,Hypergroup,fundamental relation,category
https://mir.kashanu.ac.ir/article_46681.html
https://mir.kashanu.ac.ir/article_46681_5c960eb0fb46ee957fc0f50ee9fd2d21.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
3
2
2018
12
01
On the Finite Groups that all Their Semi-Cayley Graphs are Quasi-Abelian
131
134
EN
Majid
Arezoomand
0000-0002-4614-6350
University of Larestan,
Larestan, I. R. Iran
arezoomand@lar.ac.ir
10.22052/mir.2019.127665.1101
In this paper, we prove that every semi-Cayley graph over a group G is quasi-abelian if and only if G is abelian.
Semi-Cayley graph,quasi-abelian,semi-regular
https://mir.kashanu.ac.ir/article_87320.html
https://mir.kashanu.ac.ir/article_87320_869503634049640f029261cb68914de1.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
3
2
2018
12
01
On the Regular Power Graph on the Conjugacy Classes of Finite Groups
135
138
EN
Sajjad
Mahmood Robati
Department of Mathematics, Faculty of science, Imam Khomeini international University
sajjad.robati@gmail.com
10.22052/mir.2019.172618.1118
The (undirected) power graph on the conjugacy classes <em>P</em><sub>C</sub>(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 <em>P</em><sub>C</sub>(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.
Power graph,finite group,Conjugacy classes
https://mir.kashanu.ac.ir/article_88414.html
https://mir.kashanu.ac.ir/article_88414_ff1c56177711f42e8c43d4466df2e617.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
3
2
2018
12
01
Classification of Monogenic Ternary Semigroups
139
146
EN
Nahid
Ashrafi
Faculty of Mathematics, Statistics and Computer Science
Semnan University
Semnan, Iran
nashrafi@semnan.ac.ir
Zahra
Yazdanmehr
Faculty of Mathematics, Statistics and Computer Science
Semnan University
Semnan, Iran
zhyazdanmehr@gmail.com
10.22052/mir.2019.173544.1120
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.
Ternary semigroup,monogenic ternary semigroup,Index,Period
https://mir.kashanu.ac.ir/article_88436.html
https://mir.kashanu.ac.ir/article_88436_9d35edfa9b15675083a1676c24fd7b68.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
3
2
2018
12
01
1-Designs from the group PSL2(59) and their automorphism groups
147
158
EN
Reza
Kahkeshani
Department of Pure Mathematics,
Faculty of Mathematical Sciences,
University of Kashan,
Kashan, 87317-53153
I. R. Iran
kahkeshanireza@kashanu.ac.ir
10.22052/mir.2017.68740.1048
In this paper, we consider the projective special linear group PSL<sub>2(59) </sub>and construct some 1-designs by applying the Key-Moori method on PSL<sub>2(59)</sub>. Moreover, we obtain parameters of these designs and their automorphism groups. It is shown that PSL<sub>2(59)</sub> and PSL<sub>2(59)</sub>:2 appear as the automorphism group of the constructed designs.
design,Automorphism group,Projective special linear group
https://mir.kashanu.ac.ir/article_88470.html
https://mir.kashanu.ac.ir/article_88470_659870553713da42a799e50be9b8af81.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
3
2
2018
12
30
(c,1,...,1) Polynilpotent Multiplier of some Nilpotent Products of Groups
159
171
EN
Azam
Kaheni
Department of Mathematics, University of Birjand,
Birjand 615-97175, I. R. Iran
azamkaheni@birjand.ac.ir
Saeed
Kayvanfar
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
skayvanf@um.ac.ir
10.22052/mir.2019.190182.1150
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).
Baer invariant,nilpotent product,basic commutator
https://mir.kashanu.ac.ir/article_89271.html
https://mir.kashanu.ac.ir/article_89271_6011d9b20decc8781cd94b0c49778d84.pdf