Monomorphism in one of the component of pushout diagram implies other component is monomorphism

Question

http://presheaf.com/cache/d1h3rn191q292q485j3424g45423d55.png

Here our category is that of groups where first arrow between A and B is a monomorphism. Does that imply that the lower bottom arrow is a monomorphism ? That is the arrow between B and C. Here the diagram is a pushout diagram.