eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2018-12-01
3
2
81
87
10.22052/mir.2018.97876.1078
64768
An Improved Hash Function Based on the Tillich-Zémor Hash Function
Ahmad Gaeini
againi@ihu.ac.ir
1
Mohammad Hossein Ghaffari
mhghaffari@alumni.iust.ac.ir
2
Zohreh Mostaghim
mostaghim@iust.ac.ir
3
Department of Mathematics, Faculty of Science, Imam Hossein Comprehensive University, Tehran, I. R. Iran
Department of Mathematics, Faculty of Science, Imam Hossein Comprehensive University, Tehran, I. R. Iran
Cryptography and Data Security Laboratory, School of Mathematics, Iran University of Science and Technology, Tehran, I. R. Iran
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.
http://mir.kashanu.ac.ir/article_64768_8e0dcee67425dfa7e0e5eb3b16640267.pdf
The Tillich-Zemor hash function
Cayley hash function
special linear group
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2018-12-01
3
2
89
98
10.22052/mir.2017.62726.1044
45273
A Simple Classification of Finite Groups of Order p2q2
Aziz Seyyed Hadi
aziz.saidhadi@gmail.com
1
Modjtaba Ghorbani
mghorbani@srttu.edu
2
Farzaneh Nowroozi Larki
fnowroozi@gmail.com
3
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University
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.
http://mir.kashanu.ac.ir/article_45273_e39c942af529952ba55f29606887d4c6.pdf
Semi-direct product
p-group
Sylow subgroup
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2018-12-01
3
2
99
108
10.22052/mir.2017.56003.1035
45109
Some Structural Properties of Upper and Lower Central Series of Pairs of Groups
Azam Kaheni
azam.kaheni@stu-mail.um.ac.ir
1
Saeed Kayvanfar
skayvanf@um.ac.ir
2
Ferdowsi University of Mashhad
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
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.
http://mir.kashanu.ac.ir/article_45109_b22684cd6fd03b64d74b22ff07832283.pdf
n-Isoclinism
pair of groups
Quotient irreducible pair
pi-groups
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2018-12-01
3
2
109
115
10.22052/mir.2019.186347.1133
88262
Groups with Two Extreme Character Degrees and their Minimal Faithful Representations
Mahtab Delfani
ma.delfani@gmail.com
1
Houshang Behravesh
h.behravesh@gmail.com
2
Department of Mathematics, Urmia University, Urmia, Iran
Department of Mathematics, Urmia University, Urmia, Iran
for a finite group G, we denote by p(G) the minimal degree of faithful permutation<br /> representations of G, and denote by c(G), the minimal degree of faithful representation of G by<br /> quasi-permutation matrices over the complex field C. In this paper we will assume that, G is a<br /> p-group of exponent p and class 2, where p is prime and cd(G) = {1, |G : Z(G)|^1/2}. Then we will<br /> show that<br /> c(G)≤ |G : Z(G)|^{1/2} c(Z(G)) , p(G) ≤ |G : Z(G)|^{1/2}p(Z(G)):
http://mir.kashanu.ac.ir/article_88262_bbea5fc48f8ecb778827001fced83bbd.pdf
quasi-permutation
Linear character
Non-linear character
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2018-12-01
3
2
117
129
10.22052/mir.2017.46681
46681
Fundamental Functor Based on Hypergroups and Groups
Mohammad Hamidi
m.hamidi@pnu.ac.ir
1
Department of Mathematics, Payame Noor University, Tehran, I. R. Iran
The purpose of this paper is to compute of fundamental relations<br /> of hypergroups. In this regards first we study some basic properties of<br /> fundamental relation of hypergroups, then we show that any given group is<br /> isomorphic to the fundamental group of a nontrivial hypergroup. Finally we<br /> study the connections between categories of hypergroups and groups via the<br /> fundamental relatio
http://mir.kashanu.ac.ir/article_46681_5c960eb0fb46ee957fc0f50ee9fd2d21.pdf
Group
Hypergroup
fundamental relation
category
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2018-12-01
3
2
131
134
10.22052/mir.2019.127665.1101
87320
On the Finite Groups that all Their Semi-Cayley Graphs are Quasi-Abelian
Majid Arezoomand
arezoomand@lar.ac.ir
1
University of Larestan
In this paper, we prove that every semi-Cayley graph over a group G is quasi-abelian if and only if G is abelian.
http://mir.kashanu.ac.ir/article_87320_869503634049640f029261cb68914de1.pdf
Semi-Cayley graph
quasi-abelian
semi-regular
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2018-12-01
3
2
135
138
10.22052/mir.2019.172618.1118
88414
On the Regular Power Graph on the Conjugacy Classes of Finite Groups
Sajjad Mahmood Robati
sajjad.robati@gmail.com
1
Department of Mathematics, Faculty of science, Imam Khomeini international University
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 $k=5,6$.
http://mir.kashanu.ac.ir/article_88414_ff1c56177711f42e8c43d4466df2e617.pdf
Power graph
finite group
Conjugacy classes
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2018-12-01
3
2
139
146
10.22052/mir.2019.173544.1120
88436
Classification of Monogenic Ternary Semigroups
Nahid Ashrafi
nashrafi@semnan.ac.ir
1
Zahra Yazdanmehr
zhyazdanmehr@gmail.com
2
Faculty of Mathematics, Statistics and Computer Science Semnan University Semnan, Iran
Faculty of Mathematics, Statistics and Computer Science Semnan University Semnan, Iran
The aim of this paper is to classify all monogenic ternary semigroups,<br /> up to isomorphism. We divide them to two groups: finite and infinite.<br /> We show that every infinite monogenic ternary semigroup is isomorphic to<br /> the ternary semigroup O, the odd positive integers with ordinary addition.<br /> Then we prove that all finite monogenic ternary semigroups with the same<br /> index and the same period are isomorphic. We also investigate structure of<br /> finite monogenic ternary semigroups and we prove that any finite monogenic<br /> ternary semigroup is isomorphic to a quotient ternary semigroup.
http://mir.kashanu.ac.ir/article_88436_9d35edfa9b15675083a1676c24fd7b68.pdf
Ternary semigroup
monogenic ternary semigroup
Index
Period
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2018-12-01
3
2
147
158
10.22052/mir.2017.68740.1048
88470
1-Designs from the group $PSL_{2}(59)$ and their automorphism groups
Reza Kahkeshani
kahkeshanireza@kashanu.ac.ir
1
University of Kashan
In this paper, we consider the projective special linear group $PSL_2(59)$<br /> and construct some 1-designs by applying the Key-Moori method on $PSL_2(59)$. <br /> Moreover, we obtain parameters of these designs and their automorphism groups. <br /> It is shown that $PSL_2(59)$ and $PSL_2(59):2$ appear as the automorphism group of the constructed designs.
http://mir.kashanu.ac.ir/article_88470_659870553713da42a799e50be9b8af81.pdf
05E15
05E20
05B05
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2018-12-30
3
2
159
171
10.22052/mir.2019.190182.1150
89271
(c,1,...,1) Polynilpotent Multiplier of some Nilpotent Products of Groups
Azam Kaheni
azamkaheni@birjand.ac.ir
1
Saeed Kayvanfar
skayvanf@um.ac.ir
2
Department of Mathematics, University of Birjand,
Birjand 615-97175, I. R. Iran
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
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).
http://mir.kashanu.ac.ir/article_89271_6011d9b20decc8781cd94b0c49778d84.pdf
Baer invariant
nilpotent product
basic commutator