Homotopy Category of Cotorsion Flat Representations of Quivers
Hossein
Eshraghi
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, I. R. Iran
author
text
article
2020
eng
Recently in [10], it was proved that over any ring R, there exists a complete cotorsion pair (Kp(Flat-R); K(dg-CotF-R)) in K(Flat-R), the homotopy category of complexes of flat R-modules, where Kp(Flat-R) and K(dg-CotF-R) are the homotopy categories raised by flat (or pure) and dgcotorsion complexes of flat R-modules, respectively. This paper aims at recognition of a parallel cotorsion pair in K(Flat-Q), the homotopy category of flat representation of certain quivers Q, where Q may also be infinite. The importance of this result lies in the fact that this homotopy categories do not necessarily raise from the category of modules over some ring. In the other part of this paper, we give a classification of compact objects in K(dg-CotF-Q), the homotopy category of dg-cotorsion complexes of flat representations of certain Q, in terms of the corresponding vertex-complexes
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
5
v.
4
no.
2020
279
294
https://mir.kashanu.ac.ir/article_110817_adb30153d64d87e593e5843f8eb85101.pdf
dx.doi.org/10.22052/mir.2020.237654.1219
On the Entropy Rate of a Random Walk on t-Designs
Reza
Kahkeshani
Department of Pure Mathematics,
Faculty of Mathematical Sciences, University of Kashan, Kashan, I. R. Iran
author
text
article
2020
eng
In this paper, a random walk on t-designs are considered. We assign a weight to each block and walk randomly on the vertices with a probability proportional to the weight of blocks. This stochastic process is a Markov chain. We obtain a stationary distribution for this process and compute its entropy rate. It is seen that, when the blocks have the same weight, the uniform distribution on the vertices is a stationary distribution and the entropy rate depends only on the number of vertices.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
5
v.
4
no.
2020
295
301
https://mir.kashanu.ac.ir/article_110784_434d9ff15d7d3aedacef7e70a559e573.pdf
dx.doi.org/10.22052/mir.2020.233084.1214
Planarity of Inclusion Graph of Cyclic Subgroups of Finite Group
Zahra
Garibbolooki
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, I. R. Iran
author
Sayyed Heidar
Jafari
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, I. R. Iran
author
text
article
2020
eng
Let G be a finite group. The inclusion graph of cyclic subgroups of G, Ic(G), is the (undirected) graph with vertices of all cyclic subgroups of G, and two distinct cyclic subgroups ⟨a⟩ and ⟨b⟩, are adjacent if and only if ⟨a⟩ ⊂ ⟨b⟩ or ⟨b⟩ ⊂ ⟨a⟩. In this paper, we classify all finite abelian groups, whose inclusion graph is planar. Also, we study planarity of this graph for finite group G, where |π(Z(G))| ≥ 2.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
5
v.
4
no.
2020
303
314
https://mir.kashanu.ac.ir/article_110818_50d9a27f16616352a203bb78c86e1f9f.pdf
dx.doi.org/10.22052/mir.2020.209251.1183
On Vertex-Uniprimitive Non-Cayley Graphs of Order pq
Mohammad Ali
Iranmanesh
Department of Mathematical Science, Yazd University, Yazd, 89195-741, I. R. Iran
author
text
article
2020
eng
Let p and q be distinct odd primes. Let Γ = (V (Γ),E(Γ)) be a non-Cayley vertex-transitive graph of order pq. Let G ≤ Aut(Γ) acts primitively on the vertex set V (Γ). In this paper, we show that G is uniprimitive which is primitive but not 2-transitive and we obtain some information about p,q and the minimality of the Socle T = Soc(G)
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
5
v.
4
no.
2020
315
319
https://mir.kashanu.ac.ir/article_110819_2f9cf57410bdcf1a32da73d1f6251cb4.pdf
dx.doi.org/10.22052/mir.2020.240329.1249
F-Hypergroups of Type U on the Right
Mehdi
Farshi
Department of Mathematics, Yazd University, Yazd, I. R. Iran
author
Bijan
Davvaz
Department of Mathematics, Yazd University, Yazd, I. R. Iran
author
Fatemeh
Dehghan
Department of Mathematics, Yazd University, Yazd, I. R. Iran
author
text
article
2020
eng
In this paper, first we introduce F-hypergroups of type U on the right. We will prove that every right scalar identity of an F-hypergroup of type U on the right of size ≤ 5 is also a left identity. Also, we will classify F-hypergroups of type U on the right of order 2 or 3 up to an isomorphism. Then, we will study cyclic F-semihypergroups and finally by using regular relations we construct right reversible quotient F-hypergroups.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
5
v.
4
no.
2020
321
344
https://mir.kashanu.ac.ir/article_110820_5d8c41fa477b97bf10307693662586f4.pdf
dx.doi.org/10.22052/mir.2020.240327.1248
n-capability of A-groups
Marzieh
Chakaneh
Department of Pure Mathematics,
Ferdowsi University of Mashhad,
P. O. Box 1159, Mashhad 91775, I. R. Iran
author
Saeed
Kayvanfar
Department of Pure Mathematics,
Ferdowsi University of Mashhad,
P. O. Box 1159, Mashhad 91775, I. R. Iran
author
Rasoul
Hatamian
Department of Pure Mathematics,
Payame Noor University,
Tehran, I. R. Iran
author
text
article
2020
eng
Following P. Hall a soluble group whose Sylow subgroups are all abelian is called A-group. The purpose of this article is to give a new and shorter proof for a criterion on the capability of A-groups of order p2q, where p and q are distinct primes. Subsequently we give a sufficient condition for n-capability of groups having the property that their center and derived subgroups have trivial intersection, like the groups with trivial Frattini subgroup and A-groups. An interesting necessary and sufficient condition for capability of the A-groups of square free order will be also given.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
5
v.
4
no.
2020
345
353
https://mir.kashanu.ac.ir/article_110821_0abe1545736a161f9fd287d64f272d75.pdf
dx.doi.org/10.22052/mir.2020.240334.1251
On n-Nilpotent Groups and n-Nilpotency of n-Abelian Groups
Azam
Pourmirzaei
Department of Mathematics, Hakim Sabzevari University, Sabzevar, I. R. Iran
author
Yaser
Shakourie
Department of Mathematics,
Hakim Sabzevari University,
Sabzevar, I. R. Iran
author
text
article
2020
eng
The concept of n-nilpotent groups was introduced by Moghaddam and Mashayekhy in 1991 which is in a way a generalized version of the notion of nilpotent groups. Using the n-center subgroup, a new series was constructed, which is a generalization of the upper central series of a group. In this article some properties of such groups will be studied. Finally more results for an n-nilpotent group G are given based on the assumption that G is n-abelian.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
5
v.
4
no.
2020
355
366
https://mir.kashanu.ac.ir/article_111284_8d26176dc2c9950de88884bb0c1ef355.pdf
dx.doi.org/10.22052/mir.2020.240324.1245
On Nilpotent Multipliers of Pairs of Groups
Azam
Hokmabadi
Department of Mathematics, Faculty of Sciences, Payame Noor University, 19395-4697 Tehran, I. R. Iran
author
Fahimeh
Mohammadzadeh
Department of Mathematics, Faculty of Sciences, Payame Noor University, 19395-4697 Tehran, I. R. Iran
author
Behrooz
Mashayekhy
Department of Pure Mathematics,
Center of Excellence in Analysis on Algebraic Structures,
Ferdowsi University of Mashhad,
P.O.Box 1159-91775, Mashhad,
Iran
author
text
article
2020
eng
In this paper, we determine the structure of the nilpotent multipliers of all pairs (G,N) of finitely generated abelian groups where N admits a complement in G. Moreover, some inequalities for the nilpotent multipliers of pairs of finite groups and their factor groups are given.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
5
v.
4
no.
2020
367
377
https://mir.kashanu.ac.ir/article_111342_53e46a479d32835bd5501c1cc88bd6b2.pdf
dx.doi.org/10.22052/mir.2020.240332.1250
Commuting Conjugacy Class Graph of G when G / Z(G)~=D2n
Mohammad Ali
Salahshour
Department of Mathematics, Savadkooh Branch, Islamic Azad University, Savadkooh, Iran.
author
text
article
2020
eng
Suppose G is a finite non-abelian group and Γ(G) is a simple graph with the non-central conjugacy classes of G as its vertex set. Two different noncentral conjugacy classes C and B are assumed to be adjacent in Γ(G) if and only if there are elements a ∈ A and b ∈ B such that ab = ba. This graph is called the commuting conjugacy class graph of G. In this paper, the structure of the commuting conjugacy class graph of a group G with this property that Z(G)/G≅D_{2n} will be determined.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
5
v.
4
no.
2020
379
385
https://mir.kashanu.ac.ir/article_111344_82ed25c1a987eaa08d9cb5c17b0c11b2.pdf
dx.doi.org/10.22052/mir.2021.240226.1232