Is it permissible for a woman to return to her first husband, who divorced her three times, after she has married another man and engaged in sexual intercourse with him only once?

If the suitor has performed a valid marriage contract with you and had intercourse with you after the contract, then divorced you, and your waiting period has ended, then your first husband is permitted to contract a new marriage with you. The intercourse that occurred after the contract and before the wedding does not prevent the validity of returning to the first husband.