Is it permissible for a woman to offer the greeting of Islam to men, whether they are men only or mixed with men and women?

It is permissible for a woman to greet men with salaam, and vice versa, provided there is no fear of temptation (fitna). Some scholars have held it permissible with elderly women but not with young women. It is better for young women to avoid it to avoid disagreement. However, if there is a fear of temptation, it is forbidden by consensus.