2020-07-14T14:27:44Z
http://mir.kashanu.ac.ir/?_action=export&rf=summon&issue=6854
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2018
3
2
A Tribute to Mohammad Reza Darafsheh
Ali Reza
Ashrafi
Khadijeh
Fathalikhani
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.<br />
Computational group theory
Character theory
Combinatorics
2018
12
01
75
79
http://mir.kashanu.ac.ir/article_88205_18143ed81980d0d5bfb4bdf84528f0de.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2018
3
2
An Improved Hash Function Based on the Tillich-Zémor Hash Function
Ahmad
Gaeini
Mohammad Hossein
Ghaffari
Zohreh
Mostaghim
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
2018
12
01
81
87
http://mir.kashanu.ac.ir/article_64768_8e0dcee67425dfa7e0e5eb3b16640267.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2018
3
2
A Simple Classification of Finite Groups of Order p2q2
Aziz
Seyyed Hadi
Modjtaba
Ghorbani
Farzaneh
Nowroozi Larki
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.
Semi-direct product
p-group
Sylow subgroup
2018
12
01
89
98
http://mir.kashanu.ac.ir/article_45273_e39c942af529952ba55f29606887d4c6.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2018
3
2
Some Structural Properties of Upper and Lower Central Series of Pairs of Groups
Azam
Kaheni
Saeed
Kayvanfar
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
2018
12
01
99
108
http://mir.kashanu.ac.ir/article_45109_b22684cd6fd03b64d74b22ff07832283.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2018
3
2
Groups with Two Extreme Character Degrees and their Minimal Faithful Representations
Mahtab
Delfani
Houshang
Behravesh
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)):
quasi-permutation
Linear character
Non-linear character
2018
12
01
109
115
http://mir.kashanu.ac.ir/article_88262_bbea5fc48f8ecb778827001fced83bbd.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2018
3
2
Fundamental Functor Based on Hypergroups and Groups
Mohammad
Hamidi
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
Group
Hypergroup
fundamental relation
category
2018
12
01
117
129
http://mir.kashanu.ac.ir/article_46681_5c960eb0fb46ee957fc0f50ee9fd2d21.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2018
3
2
On the Finite Groups that all Their Semi-Cayley Graphs are Quasi-Abelian
Majid
Arezoomand
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
2018
12
01
131
134
http://mir.kashanu.ac.ir/article_87320_869503634049640f029261cb68914de1.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2018
3
2
On the Regular Power Graph on the Conjugacy Classes of Finite Groups
Sajjad
Mahmood Robati
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 $k=5,6$.
Power graph
finite group
Conjugacy classes
2018
12
01
135
138
http://mir.kashanu.ac.ir/article_88414_ff1c56177711f42e8c43d4466df2e617.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2018
3
2
Classification of Monogenic Ternary Semigroups
Nahid
Ashrafi
Zahra
Yazdanmehr
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.
Ternary semigroup
monogenic ternary semigroup
Index
Period
2018
12
01
139
146
http://mir.kashanu.ac.ir/article_88436_9d35edfa9b15675083a1676c24fd7b68.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2018
3
2
1-Designs from the group $PSL_{2}(59)$ and their automorphism groups
Reza
Kahkeshani
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.
05E15
05E20
05B05
2018
12
01
147
158
http://mir.kashanu.ac.ir/article_88470_659870553713da42a799e50be9b8af81.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2018
3
2
(c,1,...,1) Polynilpotent Multiplier of some Nilpotent Products of Groups
Azam
Kaheni
Saeed
Kayvanfar
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
2018
12
30
159
171
http://mir.kashanu.ac.ir/article_89271_6011d9b20decc8781cd94b0c49778d84.pdf