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We introduce the notion of weak commensurabilty of arithmetic subgroups andrelate it to the length equivalence and isospectrality of locally symmetricspaces. We prove many strong consequences of weak commensurabilty and derivefrom these many interesting results about isolength and isospectral locallysymmetric spaces.

Weakly commensurable arithmetic groups, lengths of closed geodesics and isospectral locally symmetric spaces