Owner of the condo unit verbally promised that the tenant can have a pet. But the building management says no.

Condos or coops have bylaws that may have different rules for owners and renters. So they may allow owners to keep pets (the thinking behind that is owners will take better care of their properties than their renters will) but deny that privilege to their tenants. In both condos or coops, the board establishes rules that all owners and tenants in that building must follow. So any verbal assurance other than what's written in the lease means nothing. Always make sure to read the building's bylaws or house rules before renting a unit in a condo or coop to prevent any future surprises.