@article {
author = {Eshraghi, Hossein},
title = {Homotopy Category of Cotorsion Flat Representations of Quivers},
journal = {Mathematics Interdisciplinary Research},
volume = {5},
number = {4},
pages = {279-294},
year = {2020},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2020.237654.1219},
abstract = {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},
keywords = {Homotopy category,Cotorsion pair,compact object,Representations of a Quiver},
url = {https://mir.kashanu.ac.ir/article_110817.html},
eprint = {https://mir.kashanu.ac.ir/article_110817_adb30153d64d87e593e5843f8eb85101.pdf}
}
@article {
author = {Kahkeshani, Reza},
title = {On the Entropy Rate of a Random Walk on t-Designs},
journal = {Mathematics Interdisciplinary Research},
volume = {5},
number = {4},
pages = {295-301},
year = {2020},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2020.233084.1214},
abstract = {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.},
keywords = {random walk,Markov chain,design,entropy rate,stationary distribution},
url = {https://mir.kashanu.ac.ir/article_110784.html},
eprint = {https://mir.kashanu.ac.ir/article_110784_434d9ff15d7d3aedacef7e70a559e573.pdf}
}
@article {
author = {Garibbolooki, Zahra and Jafari, Sayyed Heidar},
title = {Planarity of Inclusion Graph of Cyclic Subgroups of Finite Group},
journal = {Mathematics Interdisciplinary Research},
volume = {5},
number = {4},
pages = {303-314},
year = {2020},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2020.209251.1183},
abstract = {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.},
keywords = {Inclusion graph,Power graph,planarity,abelian group},
url = {https://mir.kashanu.ac.ir/article_110818.html},
eprint = {https://mir.kashanu.ac.ir/article_110818_50d9a27f16616352a203bb78c86e1f9f.pdf}
}
@article {
author = {Iranmanesh, Mohammad Ali},
title = {On Vertex-Uniprimitive Non-Cayley Graphs of Order pq},
journal = {Mathematics Interdisciplinary Research},
volume = {5},
number = {4},
pages = {315-319},
year = {2020},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2020.240329.1249},
abstract = {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)},
keywords = {uniprimitive group,non-Cayley graph,socle},
url = {https://mir.kashanu.ac.ir/article_110819.html},
eprint = {https://mir.kashanu.ac.ir/article_110819_2f9cf57410bdcf1a32da73d1f6251cb4.pdf}
}
@article {
author = {Farshi, Mehdi and Davvaz, Bijan and Dehghan, Fatemeh},
title = {F-Hypergroups of Type U on the Right},
journal = {Mathematics Interdisciplinary Research},
volume = {5},
number = {4},
pages = {321-344},
year = {2020},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2020.240327.1248},
abstract = {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.},
keywords = {F-hypergroup of type U on the right,regular relation,right reversible,cyclic F-semihypergroup},
url = {https://mir.kashanu.ac.ir/article_110820.html},
eprint = {https://mir.kashanu.ac.ir/article_110820_5d8c41fa477b97bf10307693662586f4.pdf}
}
@article {
author = {Chakaneh, Marzieh and Kayvanfar, Saeed and Hatamian, Rasoul},
title = {n-capability of A-groups},
journal = {Mathematics Interdisciplinary Research},
volume = {5},
number = {4},
pages = {345-353},
year = {2020},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2020.240334.1251},
abstract = {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.},
keywords = {n-Capable group,Sylow subgroup,Frattini subgroup},
url = {https://mir.kashanu.ac.ir/article_110821.html},
eprint = {https://mir.kashanu.ac.ir/article_110821_0abe1545736a161f9fd287d64f272d75.pdf}
}
@article {
author = {Pourmirzaei, Azam and Shakourie, Yaser},
title = {On n-Nilpotent Groups and n-Nilpotency of n-Abelian Groups},
journal = {Mathematics Interdisciplinary Research},
volume = {5},
number = {4},
pages = {355-366},
year = {2020},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2020.240324.1245},
abstract = {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.},
keywords = {nilpotent group,n-abelian group,n-center subgroup,n-potent subgroup},
url = {https://mir.kashanu.ac.ir/article_111284.html},
eprint = {https://mir.kashanu.ac.ir/article_111284_8d26176dc2c9950de88884bb0c1ef355.pdf}
}
@article {
author = {Hokmabadi, Azam and Mohammadzadeh, Fahimeh and Mashayekhy, Behrooz},
title = {On Nilpotent Multipliers of Pairs of Groups},
journal = {Mathematics Interdisciplinary Research},
volume = {5},
number = {4},
pages = {367-377},
year = {2020},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2020.240332.1250},
abstract = {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.},
keywords = {pair of groups,Nilpotent multiplier,Finitely generated abelian groups},
url = {https://mir.kashanu.ac.ir/article_111342.html},
eprint = {https://mir.kashanu.ac.ir/article_111342_53e46a479d32835bd5501c1cc88bd6b2.pdf}
}
@article {
author = {Salahshour, Mohammad Ali},
title = {Commuting Conjugacy Class Graph of G when G / Z(G)~=D2n},
journal = {Mathematics Interdisciplinary Research},
volume = {5},
number = {4},
pages = {379-385},
year = {2020},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2021.240226.1232},
abstract = {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.},
keywords = {Commuting conjugacy class graph,Conjugacy classes,Center,Centralizer,Normalizer,CA-Group},
url = {https://mir.kashanu.ac.ir/article_111344.html},
eprint = {https://mir.kashanu.ac.ir/article_111344_82ed25c1a987eaa08d9cb5c17b0c11b2.pdf}
}