such a pair may also be written as Q ∨ (S ∩ T) = S ∩ (Q ∨ T), which is the equation that defines a modular lattice if it holds for any three elements of the lattice with Q ≤ S. In particular, since normal subgroups permute with each other, they form a modular sublattice. A group in which every subgroup permutes is called an Iwasawa group. The subgroup lattice of an Iwasawa group is thus a modular lattice, so these groups are sometimes called modular groups (although this latter term may have other meanings.) The assumption in the modular law for groups (as formulated above) that Q is a subgroup of S is essential. If Q is not a subgroup of S, then the tentative, more general distributive property that one may consider S ∩ (QT) = (S ∩ Q)(S ∩ T) is false. Product of subgroups with trivial intersection In particular, if S and T intersect only in the identity, then every element of ST has a unique expression as a product st with s in S and t in T. If S and T also commute, then ST is a group, and is called a Zappa–Szép product. Even further, if S or T is normal in ST, then ST coincides with the semidirect product of S and T. Finally, if both S and T are normal in ST, then ST coincides with the direct product of S and T. If S and T are subgroups whose intersection is the trivial subgroup (identity element) and additionally ST = G, then S is called a complement of T and vice versa. By a (locally unambiguous) abuse of terminology, two subgroups that intersect only on the (otherwise obligatory) identity are sometimes called disjoint. Product of subgroups with non-trivial intersection A question that arises in the case of a non-trivial intersection between a normal subgroup N and a subgroup K is what is the structure of the quotient NK/N. Although one might be tempted to just "cancel out" N and say the answer is K, that is not correct because a homomorphism with kernel N will also "collapse" (map to 1) all elements of K that happen to be in N. Thus the correct answer is that NK/N is isomorphic with K/(N∩K). This fact is sometimes called the second isomorphism theorem, (although the numbering of these theorems sees some variation