Additional Study Information: The main purpose of this clinical trial is to study women like you who have cancer cells in the lymph nodes at the time that the breast cancer is diagnosed and have chemotherapy before surgery that clears the cancer cells from the lymph nodes. This study asks 1) if, after lumpectomy, radiation to the breast and lymph nodes will be better than radiation only to the breast at keeping breast cancer from returning, and 2) if, after mastectomy, radiation to the area where the breast used to be and to the lymph nodes is better than no radiation at keeping breast cancer from returning. This study also asks whether giving radiation as described above will help women live longer.