Geodesic
On the Cohen--Lusk theorem
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 8, pp. 61-67

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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. 
@article{FPM_2007_13_8_a3,
     author = {A. Yu. Volovikov},
     title = {On the {Cohen--Lusk} theorem},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {61--67},
     publisher = {mathdoc},
     volume = {13},
     number = {8},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2007_13_8_a3/}
}
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A. Yu. Volovikov. On the Cohen--Lusk theorem. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 8, pp. 61-67. http://geodesic.mathdoc.fr/item/FPM_2007_13_8_a3/