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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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\jour J. Math. Sci.
\yr 2009
\vol 159
\issue 6
\pages 790--793
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