Is it permissible for a man to greet a woman with "salam"?

A man greeting a woman with salaam is permissible when there is no fear of temptation (fitna). However, if the woman is beautiful and there is a fear of being tempted by her, then the man should not greet her, and it is not permissible for her to return the salaam if he were to greet her, nor should she initiate the greeting to him. But if she is an old woman by whom there is no fear of temptation, then it is permissible for her to greet a man, and for him to return her salaam. It is also permissible for a man to greet a group of women, or for a group of men to greet a single woman, as long as there is no fear of temptation. As for a man shaking hands with a woman, that has a different ruling.