Is it permissible to alert the Imam if he makes a mistake in prayer by pushing or nudging?

The Sunnah for someone who wants to alert the Imam to a mistake in prayer is for a man to say "Subhanallah" (Tasbeeh), and for a woman to clap, based on the Prophet's (peace be upon him) saying: "Whoever experiences something during his prayer, let him say 'Subhanallah,' for when he says 'Subhanallah,' attention will be drawn to him. As for clapping, it is for women." As for alerting by a subtle nudge (ghamz), there is no harm in it if the congregant is close to the Imam, and the Imam is not bothered by it, and it is a slight movement; this is based on what was narrated about the Prophet (peace be upon him) taking hold of Ibn Abbas's earlobe to alert him. However, pushing the Imam is inconceivable because it is a form of harm and bad manners. If the Imam is leading a congregation and the congregants are behind him, then alerting by a subtle nudge is not prescribed, because the intention behind it would not be understood, and it would cause confusion and bother the Imam.