"At auction" doesn't tell us anything. If it was a foreclosure, you have certain protections until the end of this year and these protections will allow you to give notice to anyone in the property to vacate.
If it was a regular auction (not a foreclosure), and the tenant has a lease, you buy the lease with the property. You can offer cash for keys, but you cannot ask the tenant to vacate before the end of the lease unless you have cause (major violation of the lease).
Give her 30 days notice
try looking at 'sites like nolo.com
cant it is his building
