The concept of an "alpha" individual has a somewhat limited value in understanding human interactions (because one person doesn't always have a set alpha or beta role, they can play one or the other in different situations). And even where it does have value, alpha status isn't really obtained through conflict, it's obtained by being the best at cooperation. (this is true for other species, as well, btw....the "aggressive alpha" behavior is more often than not over-represented, a mistake usually stemming from people looking at the behavior of captive animals rather than animals in nature).
In the scenario you describe, the "alpha" would be the person who makes good things happens for the others (i.e. makes sure everyone is comfortable and having a good time, acts as the "common denominator" everyone is friends with, everyone turns to with problems, the person who makes arrangements for parties or getaways, etc.) He/she is also the one who usually brings new people into the group, or welcomes newcomers brought in by others.
When you play this role consistently (with or without hot girls around), everyone will turn to you for it, and you will have no problem being the acting "alpha" among your group of friends, at all times.