In the Hanafi school, adhan and iqamah are not prescribed Sunnahs for women; in particular, an audible public adhan is not required of them.
Shafi‘i and Maliki discussions include permission for women to give iqamah, while public adhan is evaluated separately.
The distinction turns on public proclamation versus the call immediately preceding a prayer.
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Bab al-Adhan: The Adhan, Iqamah and Juristic Rulings
In the Hanafi school, adhan and iqamah are not prescribed Sunnahs for women; in particular, an audible public adhan is not required of them.
Shafi‘i and Maliki discussions include permission for women to give iqamah, while public adhan is evaluated separately.
The distinction turns on public proclamation versus the call immediately preceding a prayer.