In mathematics, given a group G an a normal subgroup N of G, the quotient group, or factor group, of G over N is intuitively a group that "collapses" the normal subgroup N to the identity element. The quotient group is written G/N and is usually spoken in English as G mod N (mod is short for modulo). If N is not a normal subgroup, a quotient may still be taken, but the result will not be a group; rather, it will be a homogeneous space.