Union of three proper subgroups is the whole group implies they have index two and form a flower arrangement
This result is often termed Scorza's theorem since it was first proved in a paper by Scorza.
Suppose is a group and are proper subgroups of such that the union is the whole group :
Then each has index two in , and they form a flower arrangement of subgroups:
Further, this intersection is a normal subgroup of and the quotient is isomorphic to the Klein four-group.