University of Kashan Mathematics Interdisciplinary Research 2538-3639 3 2 2018 12 01 An Improved Hash Function Based on the Tillich-Zémor Hash Function 81 87 64768 10.22052/mir.2018.97876.1078 EN Ahmad Gaeini Department of Mathematics, Faculty of Science, Imam Hossein Comprehensive University, Tehran, I. R. Iran Mohammad Hossein Ghaffari Department of Mathematics, Faculty of Science, Imam Hossein Comprehensive University, Tehran, I. R. Iran Zohreh Mostaghim Cryptography and Data Security Laboratory, School of Mathematics, Iran University of Science and Technology, Tehran, I. R. Iran Journal Article 2017 09 10 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.
University of Kashan Mathematics Interdisciplinary Research 2538-3639 3 2 2018 12 01 A Simple Classification of Finite Groups of Order p2q2 89 98 45273 10.22052/mir.2017.62726.1044 EN Aziz Seyyed Hadi Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University Modjtaba Ghorbani Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University Farzaneh Nowroozi Larki Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University Journal Article 2016 04 24 ‎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.‎
University of Kashan Mathematics Interdisciplinary Research 2538-3639 3 2 2018 12 01 Some Structural Properties of Upper and Lower Central Series of Pairs of Groups 99 108 45109 10.22052/mir.2017.56003.1035 EN Azam Kaheni Ferdowsi University of Mashhad Saeed Kayvanfar Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran Journal Article 2015 10 15 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.
University of Kashan Mathematics Interdisciplinary Research 2538-3639 3 2 2018 12 01 Groups with Two Extreme Character Degrees and their Minimal Faithful Representations 109 115 88262 10.22052/mir.2019.186347.1133 EN Mahtab Delfani Department of Mathematics, Urmia University, Urmia, Iran Houshang Behravesh Department of Mathematics, Urmia University, Urmia, Iran Journal Article 2019 05 18 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)):
University of Kashan Mathematics Interdisciplinary Research 2538-3639 3 2 2018 12 01 Fundamental Functor Based on Hypergroups and Groups 117 129 46681 10.22052/mir.2017.46681 EN Mohammad Hamidi ‎Department of Mathematics, ‎Payame Noor University‎, ‎Tehran‎, ‎I‎. ‎R‎. ‎Iran Journal Article 2016 05 30 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
University of Kashan Mathematics Interdisciplinary Research 2538-3639 3 2 2018 12 01 On the Finite Groups that all Their Semi-Cayley Graphs are Quasi-Abelian 131 134 87320 10.22052/mir.2019.127665.1101 EN Majid Arezoomand University of Larestan 0000-0002-4614-6350 Journal Article 2018 05 16 In this paper, we prove that every semi-Cayley graph over a group G is quasi-abelian if and only if G is abelian.
University of Kashan Mathematics Interdisciplinary Research 2538-3639 3 2 2018 12 01 On the Regular Power Graph on the Conjugacy Classes of Finite Groups 135 138 88414 10.22052/mir.2019.172618.1118 EN Sajjad Mahmood Robati Department of Mathematics, Faculty of science, Imam Khomeini international University Journal Article 2018 02 18 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\$.
University of Kashan Mathematics Interdisciplinary Research 2538-3639 3 2 2018 12 01 Classification of Monogenic Ternary Semigroups 139 146 88436 10.22052/mir.2019.173544.1120 EN Nahid Ashrafi Faculty of Mathematics, Statistics and Computer Science Semnan University Semnan, Iran Zahra Yazdanmehr Faculty of Mathematics, Statistics and Computer Science Semnan University Semnan, Iran Journal Article 2018 03 02 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.
University of Kashan Mathematics Interdisciplinary Research 2538-3639 3 2 2018 12 01 1-Designs from the group \$PSL_{2}(59)\$ and their automorphism groups 147 158 88470 10.22052/mir.2017.68740.1048 EN Reza Kahkeshani University of Kashan Journal Article 2016 11 23 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.
University of Kashan Mathematics Interdisciplinary Research 2538-3639 3 2 2018 12 30 (c,1,...,1) Polynilpotent Multiplier of some Nilpotent Products of Groups 159 171 89271 10.22052/mir.2019.190182.1150 EN Azam Kaheni Department of Mathematics, University of Birjand, Birjand 615-97175, I. R. Iran Saeed Kayvanfar Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran Journal Article 2018 06 01 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).