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Journal of the Australian Mathematical Society, 1966 The concept of critical group was introduced by D. C. Cross (as reported byG. Higman in [5]): a finite group is calledcriticalif it is not contained in the variety generated by its proper factors. (Thefactorsof a groupGare the groups H/K where KH ≦G, and H/K is aproper factorofGunlessH = GandK=1).
László Kovács, M. F. Newman
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A Remark on Critical Groups [PDF]
Journal of the Australian Mathematical Society, 1969 Problem 24 of Hanna Neumann's book [3] reads: Does there exist, for a given integer n > 0, a Cross variety that is generated by its k-generator groups and contains (k+n)-generator critical groups? In such a variety, is every critical group that needs more than k generators a factor of a k-generator critical group, or at least of the free group of ...
László Kovács
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Numerical renormalization group at criticality [PDF]
Physics Letters A, 1996 5 pages, LaTeX, 5 figures available upon ...
Tomotoshi Nishino +2 more
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Critical Groups of Simplicial Complexes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We generalize the theory of critical groups from graphs to simplicial complexes. Specifically, given a simplicial complex, we define a family of abelian groups in terms of combinatorial Laplacian operators, generalizing the construction of the critical ...
Art M. Duval +2 more
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The Fucik spectrum and critical groups [PDF]
Proceedings of the American Mathematical Society, 2001 We compute critical groups of zero for variational functionals arising from semilinear elliptic boundary value problems with jumping nonlinearities when the asymptotic limits of the nonlinearity fall in certain parts of Type (II) regions between curves of the Fucik spectrum.
Kanishka Perera, Martin Schechter
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The critical group of a threshold graph
Linear Algebra and its Applications, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hans Christianson, Victor Reiner
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Eigenvalues and critical groups of Adinkras
Advances in Applied Mathematics, 2023 Adinkras are signed graphs used to study supersymmetry in physics. We provide an introduction to these objects, and study the properties of their signed adjacency and signed Laplacian matrices. These matrices each have exactly two distinct eigenvalues (of equal multiplicity), making Adinkras closely related to the notions of strongly regular graphs. We
Iga, Kevin +3 more
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Multiple periodic solutions of nonlinear second order differential equations
AIMS Mathematics, 2023 In this paper, we are interested in the existence of multiple nontrivial $ T $-periodic solutions of the nonlinear second ordinary differential equation $ \ddot{x}+V_x(t, x) = 0 $ in $ N(\geq 1) $ dimensions.
Keqiang Li, Shangjiu Wang
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A multiplicity theorem for parametric superlinear (p,q)-equations [PDF]
Opuscula Mathematica, 2020 We consider a parametric nonlinear Robin problem driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation). The reaction term is \((p-1)\)-superlinear but need not satisfy the Ambrosetti-Rabinowitz condition.
Florin-Iulian Onete +2 more
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Advances in Nonlinear Analysis, 2020 We consider a nonlinear elliptic equation driven by the (p, q)–Laplacian plus an indefinite potential. The reaction is (p − 1)–superlinear and the boundary term is parametric and concave.
Papageorgiou Nikolaos S., Zhang Youpei
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