منابع مشابه
The Polynomial Functions on Frobenius Complements
We determine the number of unary polynomial functions on all Frobenius complements and on all finite solvable groups all of whose abelian subgroups are cyclic. 1. Notation and results Let (G, ·) be a group. A unary polynomial function p : G → G is a function that can be written in the form p(x) := a0x a1x e1 · · · an−1xan, where n ∈ N0, a0, . . . , an are in G, and e0, . . . , en−1 are integers...
متن کاملGroups of Prime Power Order as Frobenius-wielandt Complements
It is known that the Sylow subgroups of a Frobenius complement are cyclic or generalized quaternion. In this paper it is shown that there are no restrictions at all on the structure of the Sylow subgroups of the FrobeniusWielandt complements that appear in the well-known Wielandt's generalization of Frobenius' Theorem. Some examples of explicit constructions are also given. 0. Introduction Let ...
متن کاملBounds on generalized Frobenius numbers
Let N ≥ 2 and let 1 < a1 < · · · < aN be relatively prime integers. The Frobenius number of this N -tuple is defined to be the largest positive integer that has no representation as PN i=1 aixi where x1, ..., xN are nonnegative integers. More generally, the s-Frobenius number is defined to be the largest positive integer that has precisely s distinct representations like this. We use techniques...
متن کاملGeneralized Perron-Frobenius Theorem for Nonsquare Matrices
The celebrated Perron–Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. H...
متن کاملAn Extreme Family of Generalized Frobenius Numbers
We study a generalization of the Frobenius problem: given k positive relatively prime integers, what is the largest integer g0 that cannot be represented as a nonnegative integral linear combination of the given integers? More generally, what is the largest integer gs that has exactly s such representations? We construct a family of integers, based on a recent paper by Tripathi, whose generaliz...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1966
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1966-0201505-9