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Fundam. Prikl. Mat., 2007, Volume 13, Issue 8, Pages 61–67 (Mi fpm1108)  

On the Cohen–Lusk theorem

A. Yu. Volovikov

Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)

Abstract: Let $G$ be a finite group and $X$ be a $G$-space. For a map $f\colon X\to\mathbb R^m$, the partial coincidence set $A(f,k)$, $k\leq|G|$, is the set of points $x\in X$ such that there exist $k$ elements $g_1,…,g_k$ of the group $G$, for which $f(g_1x)=…=f(g_kx)$ hold. We prove that the partial coincidence set is nonempty for $G=\mathbb Z_p^n$ under some additional assumptions.

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English version:
Journal of Mathematical Sciences (New York), 2009, 159:6, 790–793

Bibliographic databases:

UDC: 515.14

Citation: A. Yu. Volovikov, “On the Cohen–Lusk theorem”, Fundam. Prikl. Mat., 13:8 (2007), 61–67; J. Math. Sci., 159:6 (2009), 790–793

Citation in format AMSBIB
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\paper On the Cohen--Lusk theorem
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\pages 61--67
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\jour J. Math. Sci.
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\issue 6
\pages 790--793
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