What is the ruling regarding worshipers who rose from bowing after the Imam's second takbeer, thinking that he had risen, and what should they do?

The Imam's unintended saying of "Allahu Akbar" during the bowing (ruku') does not invalidate the prayer, and the majority of scholars do not recommend for him to perform the prostration of forgetfulness (sujud al-sahw) for it. If the Imam forgets and does not perform the prostration of forgetfulness, the congregant (ma'mum) should perform it, according to the Shafi'is and Malikis. If only the congregant forgets, there is no prostration for him, rather the Imam bears it on his behalf. As for the congregants who stood up mistakenly when the Imam said "Allahu Akbar" and then realized their error, they must return to the bowing position. Their prayer is valid if they did not return until the Imam had already risen.