Totally not permitted. There is a reason why Chazal was mesaken chazoras hashatz. If they wanted people to learn during davening, there would be a seder limud in middle of davening. There is a time and place for everyting. Davening is set aside for prayer and introspection. When the chazan repeats the shemoney esray, listen with kavna and answer amain., Anyone that learns during chazoras hashatz is a fool.
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