6

May a woman, who after receiving a get from her husband has relations with another man out of wedlock, remarry her husband?

12

Both the first relationship and the second one would have to be formal marriages (the kind that requires a Get to dissolve) for the prohibition of remarrying your divorcée to come into effect. (ShA EH 10:1)

איזו גרושה מותרת לחזור לבעלה ובו ז סעיפים:

המגרש את אשתו ואח"כ זינתה מותרת לחזור לבעלה:‏
הגה וכן אם זנתה עם הראשון ונתקדשה לשני וגירשה מותרת לחזור לראשון אפי' היתה מיוחדת לו תחילה (תשו' הרא"ש כלל נ"ג ומהר"ם פאדווה סימן י"ט)‏
אבל אם נתקדשה לאחר וגירשה או מת אסורה לחזור לראשון‏
ואפילו לא נתגרשה רק מכח קול בעלמא (הרא"ש כלל ה') (וע"ל סימן ו' וע"ל סימן מ"ו סעיף ה' וסעיף ו'):‏

The one who divorces his wife, and after that she committed adultery, she is permitted to return to her husband.
Ram''a: And this is also the case if she committed adultery with the first [husband], and she was betrothed to a second [husband], and he divorces her, she is permitted to return to the first [husband], even if she was designated to him first.
Shulchan Arukh: But if she was betrothed afterwards and he divorced her, or he died, it is forbidden for her to return to the first [husband].
Ram''a: And even if she was only divorced from the power of a mere rumor.

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