• Volume 114, Issue 3

      August 2004,   pages  217-298

    • On finite groups whose every proper normal subgroup is a union of a given number of conjugacy classes

      Ali Reza Ashrafi Geetha Venkataraman

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      Let G be a finite group andA be a normal subgroup ofG. We denote by ncc(A) the number ofG-conjugacy classes ofA andA is calledn-decomposable, if ncc(A)= n. SetKG = {ncc(A)¦A ⊲ G}. LetX be a non-empty subset of positive integers. A groupG is calledX-decomposable, ifKG =X.

      Ashrafi and his co-authors [1-5] have characterized theX-decomposable non-perfect finite groups forX = {1, n} andn ≤ 10. In this paper, we continue this problem and investigate the structure ofX-decomposable non-perfect finite groups, forX = {1, 2, 3}. We prove that such a group is isomorphic to Z6, D8, Q8, S4, SmallGroup(20, 3), SmallGroup(24, 3), where SmallGroup(m, n) denotes the mth group of ordern in the small group library of GAP [11].

    • Characteristic properties of large subgroups in primary abelian groups

      Peter V Danchev

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      SupposeG is an arbitrary additively written primary abelian group with a fixed large subgroupL. It is shown thatG is (a) summable; (b) σ-summable; (c) a Σ-group; (d) pω+1-projecrive only when so isL. These claims extend results of such a kind obtained by Benabdallah, Eisenstadt, Irwin and Poluianov,Acta Math. Acad. Sci. Hungaricae (1970) and Khan,Proc. Indian Acad. Sci. Sect. A (1978).

    • Multilinear integral operators and mean oscillation

      Lanzhe Liu

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      In this paper, the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces are obtained. The operators include Calderón—Zygmund singular integral operator, fractional integral operator, Littlewood—Paley operator and Marcinkiewicz operator.

    • Superstability of the generalized orthogonality equation on restricted domains

      Soon-Mo Jung Prasanna K Sahoo

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      Chmielinski has proved in the paper [4] the superstability of the generalized orthogonality equation ¦〈f(x), f(y)〉¦ = ¦〈x,y〉¦. In this paper, we will extend the result of Chmielinski by proving a theorem: LetDn be a suitable subset of ℝn. If a function f:Dn → ℝn satisfies the inequality ∥〈f(x), f(y)〉¦ ¦〈x,y〉∥ ≤ φ(x,y) for an appropriate control function φ(x, y) and for allx, y ∈ Dn, thenf satisfies the generalized orthogonality equation for anyx, y ∈ Dn.

    • Non-linear second-order periodic systems with non-smooth potential

      Evgenia H Papageorgiou Nikolaos S Papageorgiou

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      In this paper we study second order non-linear periodic systems driven by the ordinary vectorp-Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth conditions on the potential function. Then we establish the existence of non-trivial homoclinic (to zero) solutions. Our theorem appears to be the first such result (even for smooth problems) for systems monitored by thep-Laplacian. In the last section of the paper we examine the scalar non-linear and semilinear problem. Our approach uses a generalized Landesman-Lazer type condition which generalizes previous ones used in the literature. Also for the semilinear case the problem is at resonance at any eigenvalue.

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