Gittin 84 - Giving Wives as Gifts
If a man gives his wife a Get on condition that she marries so-and-so, she should not marry so-and-so, because it looks like giving wives as gifts. If she does marry, she need not divorce. She should not marry others, because this may invalidate the Get.
"On condition that you have relations with so-and-so" is valid, because she can bribe him to marry her for a time. "On condition that you have relations with my father, or your father" is not valid, because she can not bribe the father, so it is to vex her and the Get is valid.
Purpose of the letter
Mistakes are completely mine, and final law can not be definitively deduced from the summaries. Have a great day!