Is it permissible to pray without raising the hands during it?

Not raising the hands during the takbirat (recitation of 'Allahu Akbar') in prayers does not invalidate the prayer. However, one who omits it misses out on a great good, as raising the hands has been transmitted from the Prophet, peace and blessings be upon him, by twenty-one Companions, including what the two Shaykhs (Bukhari and Muslim) narrated from Ibn Umar.