FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 8, PAGES 61-67

**On the Cohen--Lusk theorem**

A. Yu. Volovikov

Abstract

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Let $G$ be
a finite group and $X$ be a $G$-space.
For a map $f:\; X$® **R**^{m},
the partial coincidence set
$A(f,k)$,
$k$£
|G|, is the set of points $x$Î
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)
hold.
We prove that the partial coincidence set is nonempty for $G\; =$**Z**_{p}^{n}
under some additional assumptions.

Location: http://mech.math.msu.su/~fpm/eng/k07/k078/k07804h.htm

Last modified: June 13, 2008