University of KashanMathematics Interdisciplinary Research2538-36393220181201An Improved Hash Function Based on the Tillich-Zémor Hash Function81876476810.22052/mir.2018.97876.1078ENAhmadGaeiniDepartment of Mathematics, Faculty of Science,
Imam Hossein Comprehensive University,
Tehran, I. R. IranMohammad HosseinGhaffariDepartment of Mathematics, Faculty of Science,
Imam Hossein Comprehensive University,
Tehran, I. R. IranZohrehMostaghimCryptography and Data Security Laboratory, School of Mathematics,
Iran University of Science and Technology,
Tehran, I. R. IranJournal Article20170910Using 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.https://mir.kashanu.ac.ir/article_64768_8e0dcee67425dfa7e0e5eb3b16640267.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36393220181201A Simple Classification of Finite Groups of Order p2q289984527310.22052/mir.2017.62726.1044ENAzizSeyyed HadiDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training UniversityModjtabaGhorbaniDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training UniversityFarzanehNowroozi LarkiDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training UniversityJournal Article20160424Suppose 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.https://mir.kashanu.ac.ir/article_45273_e39c942af529952ba55f29606887d4c6.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36393220181201Some Structural Properties of Upper and Lower Central Series of Pairs of Groups991084510910.22052/mir.2017.56003.1035ENAzamKaheniDepartment of Pure Mathematics,
Ferdowsi University of Mashhad,
Mashhad, IranSaeedKayvanfarDepartment of Pure Mathematics,
Ferdowsi University of Mashhad,
Mashhad, IranJournal Article20151015In 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.https://mir.kashanu.ac.ir/article_45109_b22684cd6fd03b64d74b22ff07832283.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36393220181201Groups with Two Extreme Character Degrees and their Minimal Faithful Representations1091158826210.22052/mir.2019.186347.1133ENMahtabDelfaniDepartment of Mathematics, Urmia University, Urmia, IranHoushangBehraveshDepartment of Mathematics, Urmia University, Urmia, IranJournal Article20190518for 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)):https://mir.kashanu.ac.ir/article_88262_bbea5fc48f8ecb778827001fced83bbd.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36393220181201Fundamental Functor Based on Hypergroups and Groups1171294668110.22052/mir.2017.46681ENMohammadHamidiDepartment of Mathematics, Payame Noor University, Tehran, I. R. IranJournal Article20160530The 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 relatiohttps://mir.kashanu.ac.ir/article_46681_5c960eb0fb46ee957fc0f50ee9fd2d21.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36393220181201On the Finite Groups that all Their Semi-Cayley Graphs are Quasi-Abelian1311348732010.22052/mir.2019.127665.1101ENMajidArezoomandUniversity of Larestan,
Larestan, I. R. Iran0000-0002-4614-6350Journal Article20180516In this paper, we prove that every semi-Cayley graph over a group G is quasi-abelian if and only if G is abelian.https://mir.kashanu.ac.ir/article_87320_869503634049640f029261cb68914de1.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36393220181201On the Regular Power Graph on the Conjugacy Classes of Finite Groups1351388841410.22052/mir.2019.172618.1118ENSajjadMahmood RobatiDepartment of Mathematics, Faculty of science, Imam Khomeini international UniversityJournal Article20180218The (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.https://mir.kashanu.ac.ir/article_88414_ff1c56177711f42e8c43d4466df2e617.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36393220181201Classification of Monogenic Ternary Semigroups1391468843610.22052/mir.2019.173544.1120ENNahidAshrafiFaculty of Mathematics, Statistics and Computer Science
Semnan University
Semnan, IranZahraYazdanmehrFaculty of Mathematics, Statistics and Computer Science
Semnan University
Semnan, IranJournal Article20180302The 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.https://mir.kashanu.ac.ir/article_88436_9d35edfa9b15675083a1676c24fd7b68.pdfUniversity of KashanMathematics Interdisciplinary Research2538-363932201812011-Designs from the group PSL2(59) and their automorphism groups1471588847010.22052/mir.2017.68740.1048ENRezaKahkeshaniDepartment of Pure Mathematics,
Faculty of Mathematical Sciences,
University of Kashan,
Kashan, 87317-53153
I. R. IranJournal Article20161123In 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.https://mir.kashanu.ac.ir/article_88470_659870553713da42a799e50be9b8af81.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36393220181230(c,1,...,1) Polynilpotent Multiplier of some Nilpotent Products of Groups1591718927110.22052/mir.2019.190182.1150ENAzamKaheniDepartment of Mathematics, University of Birjand,
Birjand 615-97175, I. R. IranSaeedKayvanfarDepartment of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, IranJournal Article20180601In 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).https://mir.kashanu.ac.ir/article_89271_6011d9b20decc8781cd94b0c49778d84.pdf