What is sarrah?

 I have have posted a discussion where Rav Moshe is asked whether a woman can be a masgiach.

The main problem is that the Rambam says women can not have Sarrah i.e. authority over others to tell them do do things they don't want to do.

Just came across a Rashi(Sanhedrin 16a where he states that a nasi and Cohen Gadol have Sarrah

He seems to be that they have status. Thus any status- even without authority should be problematic e.g.wife

רש"י מסכת סנהדרין דף טז עמוד א
דבריו של גדול - דינו של בעל שררה, כגון נשיא וכהן גדול.