Slitherine

We had a situation last night where a Fragmented enemy BG of archers broke a BG of my Cavalry. We couldn't find any rules that stop Fragmented troops pursuing, so they promptly pursued, contacting a fresh BG of my cavalry and quickly broke. Was this correct ?

Fragmented troops are not exempted from pursuit but non shock foot never have to pursue broken mounted and if they want to pusue they have to take a CMT to do so.