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\ctrline{\bfON THE CHARACTERIZATION OF CRYSTALLOGRAPHIC GROUPS}
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\ctrline{By}
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\ctrline{Hans Samelson}
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Let $E(n)$ denote the (Lie)group of Euclidean notions of $R↑n$, i.e. 
the group isonetrues if  $R↑n$ with resepect to the distance $d(x,y) =
\leftvy-x\rightv=(\Sigma(y\downi-x\downi)\↑2)↑1/2.  A subgroup \Gamma
of $E(n)$; here uniform means that the coset space $E(n)\Gamma$ is
compact.        
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