This article is cited in 2 papers

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 $g_1,\dots,g_k$ of the group $G$, for which $f(g_1x)=\dots=f(g_kx)$ hold. We prove that the partial coincidence set is nonempty for $G=\mathbb Z_p^n$ under some additional assumptions.

UDC: 515.14

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

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