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On the Cohen–Lusk theorem

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Abstract

Let G be a finite group and X be a G-space. For a map f: X → ℝm, the partial coincidence set A(f, k), k ≤ |G|, is the set of points x ∈ X such that there exist k elements g 1,…, g k of the group G, for which f(g 1 x) = ⋅⋅⋅ = f(g k x) holds. We prove that the partial coincidence set is nonempty for G = ℤ p n under some additional assumptions.

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Authors and Affiliations

  1. Moscow State Institute of Radioengineering, Electronics and Automation (Technical University), Moscow, Russia

    A. Yu. Volovikov

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  1. A. Yu. Volovikov
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Correspondence to A. Yu. Volovikov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 8, pp. 61–67, 2007.

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Volovikov, A.Y. On the Cohen–Lusk theorem. J Math Sci 159, 790–793 (2009). https://doi.org/10.1007/s10958-009-9470-7

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  • DOI: https://doi.org/10.1007/s10958-009-9470-7

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