If there is music playing in the background can a woman sing along if men are around (because technically she’s singing in a group). For example in the car with the radio on. if a song is on and a woman wants to sing but a man is present can she still sing because it’s not just her?
Music that is playing in the background is not considered as if she is singing together with other people (otherwise one would be able to listen to any women singers, since they are always singing together with music). The music is not drowning out her voice, but emphasizing it, and it isn’t permitted. Even numerous women singing together is not allowed according to the poskim. The poskim do discuss, if a woman may sing along with other men (which was not your question) that are singing, and the poskim don’t even allow that, although some poskim permit it only in a pressing situation. See sources.
If the music is loud though and it will drown out your voice so that the men can not hear it, that would be permitted, since they can’t hear you at all.
Shevet Halevi 5-197(4), Oz Nidberu 3:71, Kinyan Torah 1:85:2, Avnei Yushfei 2:5:1, Chut Shuni Shabbos 3:page 271, Yisroel Kedoshim page 161. Sridei Aish 1:77:pages 214-219, who quotes Rav Hirsch and Rav Hildsheimer zt”l as being lenient in regard to mixed zemiros only in a pressing situation.