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Mature men are allowed to marry prepubescent girls in Islam.

The Quran in Sura 65:1, 4 says:
65:1 O Prophet, when you (and the believers) divorce women, divorce them for their prescribed waiting-period and count the waiting-period accurately . . . 4 And if you are in doubt about those of your women who have despaired of menstruation, (you should know that) their waiting period is three months, and the same applies to those who have not menstruated as yet. As for pregnant women, their period ends when they have delivered their burden. (Maududi, vol. 5, pp. 599 and 617)

Maududi correctly interprets the plain meaning of verse 4, which appears in the context of divorce:

Therefore, making mention of the waiting-period for girls who have not yet menstruated, clearly proves that it is not only permissible to give away the girl at this age but it is permissible for the husband to consummate marriage with her. Now, obviously no Muslim has the right to forbid a thing which the Qur'an has held as permissible. ...