Publication Date: 2005
Communications in Algebra (00927872)33(5)pp. 1417-1425
Let n be an integer greater than 1. A group G is said to be n-rewritable (or a Qn-group) if for every n elements x1, x 2,...,xn in G there exist distinct permutations σ and τ in Sn such that xσ(1)x σ(2)⋯xσ(n)=xτ(1)x τ(2)⋯xτ(n). In this paper, we characterize all 3-rewritable nilpotent 2-groups of class 2. Also we have found a bound for the nilpotency class of certain nilpotent 3-rewritable groups, and have shown that 3-rewritable groups satisfy a certain law. Copyright © Taylor & Francis, Inc.
Publication Date: 2009
Nonlinear Analysis, Theory, Methods and Applications (0362546X)70(6)pp. 2453-2456
In this paper, we present a best approximation theorem for set-valued mappings in hyperconvex metric spaces, which generalize the well-known result of Kirk, Sims and Yuan [W.A. Kirk, B. Sims, X.Z. Yuan, The Knaster-Kuratowski and Mazurkiewicz theory in hyperconvex metric spaces and some of its applications, Nonlinear Anal. 39 (2000) 611-627]. © 2008 Elsevier Ltd. All rights reserved.
Publication Date: 1999
Archiv der Mathematik (0003889X)73(2)pp. 104-108
In this note we prove that every infinite group G is 3-abelian (i.e. (ab)3 = a3b3 for all a, b in G) if and only if in every two infinite subsets X and Y of G there exist x ∈ X and y ∈ Y such that (xy)3 = x3y3.
Publication Date: 2025
Publications of the Research Institute for Mathematical Sciences (00345318)61(2)pp. 233-275
Extended affine root systems appear as the root systems of extended affine Lie algebras. A subclass of extended affine root systems, whose elements are called “minimal”, turns out to be of special interest, mostly because of the geometric properties of their Weyl groups; they possess the so-called presentation by conjugation. In this work, we characterize minimal extended affine root systems in terms of “minimal reflectable bases”, which resembles the concept of the “base” for finite and affine root systems. As an application, we construct elliptic Lie algebras by means of Serre-type generators and relations. © 2025 Research Institute for Mathematical Sciences, Kyoto University.
Publication Date: 2021
Journal of Algebra and its Applications (02194988)20(7)
In this paper, we study the category of finitely generated modules over a class of right 4-Nakayama artin algebras. This class of algebras appear naturally in the study of representation-finite artin algebras. First, we give a characterization of right 4-Nakayama artin algebras. Then, we classify finitely generated indecomposable right modules over right 4-Nakayama artin algebras. We also compute almost split sequences for the class of right 4-Nakayama artin algebras. © 2021 World Scientific Publishing Company.
Publication Date: 2016
Communications in Algebra (00927872)44(9)pp. 3692-3704
From Burnside's pαqβ-Theorem, it follows that any nonabelian group of order pαqβ, where p and q are primes, cannot be simple. As a main result of this article, we state and prove an analog of the mentioned theorem for commutative association schemes. © 2016, Copyright © Taylor & Francis Group, LLC.
Publication Date: 2014
Fixed Point Theory (15835022)15(1)pp. 87-98
In this paper, by making use of a new class of operators, we establish some existence results of the solution for an extended general variational inequality already considered in the literature. As application, we obtain a new coincidence point theorem in a Hilbert space setting.
Publication Date: 2000
Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova (22402926)104pp. 129-134
Let α1,…, αn be nonzero integers whose greatest common divisor is d. We prove that an infinite group G is of finite exponent dividing d if and only if for every n infinite subsets X1, …, Xn of G there exist x1 ∈ X1, …, xn ∈ Xn such that x1α1…xαnn = 1. © Rendiconti del Seminario Matematico della Università di Padova, 2000, tous droits réservés.
Publication Date: 1999
Communications in Algebra (00927872)27(11)pp. 5633-5638
In this note we show that if G is a finitely generated soluble group, then every infinite subset of G contains two elements generating a nilpotent group of class at most k if and only if G is finite by a group in which every two generator subgroup is nilpotent of class at most k.
Publication Date: 2022
Communications in Algebra (00927872)50(6)pp. 2731-2739
Let χ be a virtual (generalized) character of a finite group G and (Formula presented.) be the image of χ on (Formula presented.) The pair (Formula presented.) is said to be sharp of type L or L-sharp if (Formula presented.) If the principal character of G is not an irreducible constituent of χ, the pair (Formula presented.) is called normalized. In this paper, we first provide some counterexamples to a conjecture that was proposed by Cameron and Kiyota in 1988. This conjecture states that if (Formula presented.) is L-sharp and (Formula presented.) then the inner product (Formula presented.) is uniquely determined by L. We then prove that this conjecture is true in the case that (Formula presented.) is normalized, χ is a character of G, and L contains at least an irrational value. © 2022 Taylor & Francis Group, LLC.
Publication Date: 2013
Proceedings of the American Mathematical Society (10886826)141(3)pp. 753-762
Let X be a Noetherian scheme, K(FlatX) be the homotopy category of flat quasi-coherent OX-modules and Kp(FlatX) be the homotopy category of all flat complexes. It is shown that the pair (Kp(FlatX), K (dg- CofX)) is a complete cotorsion theory in K(FlatX), where K (dg-CofX) is the essential image of the homotopy category of dg-cotorsion complexes of flat modules. Then we study the homotopy category K(dg-Cof X). We show that in the affine case, this homotopy category is equal with the essential image of the embedding functor j*: K(ProjR) → K(FlatR) which has been studied by Neeman in his recent papers. Moreover, we present a condition for the inclusion K(dg-Cof X) ⊆ K(Cof X) to be an equality, where K(Cof X) is the essential image of the homotopy category of complexes of cotorsion flat sheaves. © 2012, American Mathematical Society.
Publication Date: 2015
Journal of Group Theory (14354446)18(1)pp. 115-131
In [1], a conjecture of J. G. Thompson for PSLn(q) was proved. It was shown that every finite group G with the property Z(G) = 1 and cs(G) = cs(PSLn(q)) is isomorphic to PSLn(q) where cs(G) is the set of conjugacy class sizes of G . In this article we improve this result for PSL2(q). In fact we prove that if cs(G) = cs(PSL2(q)), for q > 3, then G ≅ PSL2(q) x A, where A is abelian. Our proof does not depend on the classification of finite simple groups. © de Gruyter 2015.
Publication Date: 2010
Publications of the Research Institute for Mathematical Sciences (16634926)46(3)pp. 507-548
Using the well-known recognition and structural theorem(s) for root-graded Lie algebras and their universal coverings, we give a finite presentation for the universal covering algebra of a centerless Lie torus of type X not equal A, C, BC We follow a unified approach for the types under consideration
Publication Date: 2002
Communications in Algebra (00927872)30(10)pp. 4821-4826
Publication Date: 2013
Miskolc Mathematical Notes (17872405)14(1)pp. 11-17
In this paper, we present a fixed point theorem for a new type of contractive mappings. Our main result extends and unifies some well-known results in the literature. © Miskolc University Press.
Publication Date: 2010
Nonlinear Analysis, Theory, Methods and Applications (0362546X)72(5)pp. 2238-2242
We present a fixed point theorem for generalized contraction in partially ordered complete metric spaces. As an application, we give an existence and uniqueness for the solution of a periodic boundary value problem. © 2009 Elsevier Ltd. All rights reserved.
Publication Date: 2023
Miskolc Mathematical Notes (17872405)24(3)pp. 1117-1126
In this paper, we obtain a generalization of a fixed point theorem given by Popescu [O. Popescu, Comput. Math. Appl., vol. 62, no. 10, pp. 3912–3919, 2011]. An example is also given to support our main result. © (2023) Miskolc University Press
Publication Date: 2014
Journal Of Applied Mathematics (16870042)2014
We first introduce a new class of contractive mappings in the setting of metric spaces and then we present certain Greguš type fixed point theorems for such mappings. As an application, we derive certain Greguš type common fixed theorems. Our results extend Greguš fixed point theorem in metric spaces and generalize and unify some related results in the literature. An example is also given to support our main result. © 2014 Marwan A. Kutbi et al.
Publication Date: 2007
Communications in Algebra (00927872)35(12)pp. 4277-4302
We introduce a new class of possibly infinite dimensional Lie algebras and study their structural properties. Examples of this new class of Lie algebras are finite dimensional simple Lie algebras containing a nonzero split torus, affine and extended affine Lie algebras. Our results generalize well-known properties of these examples.
Publication Date: 2012
Journal of Algebra and its Applications (02194988)11(4)
For a ring derivation δ, we introduce and investigate a generalization of reduced rings and Armendariz rings which we call a δ-Armendariz ring. Various classes of δ-Armendariz rings is provided and a number of properties of this generalization are established. Radicals and minimal prime ideals of the differential polynomial ring R[x; δ], in terms of those of a δ-Armendariz R, is determined. We prove that several properties transfer between R and the differential polynomial ring R[x; δ], in case R is δ-Armendariz. © 2012 World Scientific Publishing Company.
Publication Date: 2025
Journal of Algebra and its Applications (17936829)
We change Chermak-Delgado measure slightly so that it can be used for compact groups as well. Corresponding to this new measure, a lattice of open subgroups is obtained. Then we prove that if this lattice is non-empty in a compact group G, then G has a characteristic open abelian subgroup N such that [G: N] ≤ [G: A]2 for every abelian subgroup A G. This is a generalization of the well-known Chermak-Delgado Theorem. © 2026 World Scientific Publishing Company.
Publication Date: 2003
Journal of the Australian Mathematical Society (14467887)75(3)pp. 313-324
Let R be a commutative Noetherian ring with nonzero identity and let M be a finitely generated R-module. In this paper, we prove that if an ideal I of R is generated by a u.s.d-sequence on M then the local cohomology module H Ii(M) is I-cofinite. Furthermore, for any system of ideals φ of R, we study the cofiniteness problem in the context of general local cohomology modules.
Azam, S.,
Soltani, M.B.,
Tomie, M.,
Yoshii, Y. Publication Date: 2019
Publications of the Research Institute for Mathematical Sciences (00345318)(4)
We classify the reflectable bases of root systems of types A, B and D. We give a graph- theoretical characterization of reflectable bases and count the number of reflectable bases for each type. We also give a Dynkin-type characterization of reflectable bases of root systems of types A and D. © 2019 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.
Azam, S.,
Soltani, M.B.,
Tomie, M.,
Yoshii, Y. Publication Date: 2019
Publications of the Research Institute for Mathematical Sciences (16634926)55(4)pp. 689-736
We classify the reflectable bases of root systems of types A, B and D. We give a graph-theoretical characterization of reflectable bases and count the number of reflectable bases for each type. We also give a Dynkin-type characterization of reflectable bases of root systems of types A and D.
Publication Date: 2017
Discrete Mathematics (0012365X)340(5)pp. 1116-1121
The adjacency spectrum of a graph Γ, which is denoted by Spec(Γ), is the multiset of eigenvalues of its adjacency matrix. We say that two graphs Γ and Γ′ are cospectral if Spec(Γ)=Spec(Γ′). In this paper for each prime number p, p≥23, we construct a large family of cospectral non-isomorphic Cayley graphs over the dihedral group of order 2p. © 2016 Elsevier B.V.
Publication Date: 2015
Algebra Colloquium (10053867)22(4)pp. 621-638
In this work, we study the concept of the length function and some of its combinatorial properties for the class of extended affine root systems of type A1. We introduce a notion of root basis for these root systems, and using a unique expression of the elements of the Weyl group with respect to a set of generators for the Weyl group, we calculate the length function with respect to a very specific root basis. © 2015 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Suzhou University.
