Is it permissible for a woman to say "As-salamu alaykum wa rahmatullah" (Peace be upon you and God's mercy) when entering a gathering of people, or should the greeting be in another form?

Saying the greeting of Salaam does not differ in its wording between a man and a woman. However, it is forbidden for a young woman to say Salaam to non-mahram men if there is a fear of temptation arising from her.