Periodic matrices in SL(3,Z) will be conjugated to
product of periodic matrices in SL(2,Z) by +- indentity on a third
integer direction.  Is this true? 

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Sorry, following your comments, maybe something I said is misleading. I state the original question:
   Consider a periodic automorphism $\phi$ on $Z^3$, can we find a coordinate on $Z^3$, such that $\phi$ is either  (1,0;0,A) 
 or (-1,0;0,A).