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

View as HTML     View as gif image

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 $f(g$₁x) = ... = f(g_kx) hold. We prove that the partial coincidence set is nonempty for $G\; =$Z_pⁿ under some additional assumptions.

Location: http://mech.math.msu.su/~fpm/eng/k07/k078/k07804h.htm
Last modified: June 13, 2008