Whether solemn penance should be imposed on women and clerics, and whether any priest can impose it?

Objections

Objection 1 : It would seem that solemn penance should not be imposed on women. Because, when this penance is imposed on a man, he has to cut his hair off. But this becomes not a woman, according to 1 Cor. 11:15. Therefore she should not do solemn penance.
Objection 2 : It also seems that it ought to be imposed on clerics. For it is enjoined on account of a grievous crime. Now the same sin is more grievous in a cleric than in a layman. Therefore it ought to be imposed on a cleric more than on a layman.
Objection 3 : It also seems that it can be imposed by any priest. Because to absolve in the tribunal of Penance belongs to one who has the keys. Now an ordinary priest has the keys. Therefore he can administer this penance.