abH

AbH is an acronym that appears in several unrelated domains, and there is no single universally accepted meaning. In mathematical literature, AbH is sometimes used to denote the abelianization of a subgroup H of a group G, written as Ab(H) or AbH. The abelianization is defined as the quotient H/[H,H], where [H,H] is the commutator subgroup of H. This construction yields the largest abelian quotient of H and is a standard tool in group theory and homological algebra.

In the field of computational chemistry and theoretical physics, AbH is occasionally used to refer to the ab initio Hamiltonian. This Hamiltonian represents the electronic structure problem derived from first principles, without empirical parameters, and is the starting point for many ab initio methods such as Hartree–Fock and post-Hartree–Fock theories. The notation varies by author, and AbH may appear alongside terms like H_ab_initio or simply H^AbInitio.

Beyond mathematics and physics, AbH can function as an internal acronym within organizations or projects, standing for a project name or department. Such uses are highly context-dependent and not standardized.

Because AbH is ambiguous, readers should consult the specific source to determine which meaning is intended in a given document. See also discussions on abelianization and ab initio methods for related concepts.