The monthly cycle in women concerns oestrogen and progesterone. We do produce some testosterone as well, just as men produce some oestrogen, but it is not a part of the monthly cycle. But I believe that the effect of testosterone in both women and men has only begun to be researched. It must be hard, as hormones in plenty interact with each other all the time.
I think if testesterone was part of dominance, men especially would loose interest in domination as time goes by and the testesterone levels fall, and that is not the case :-)