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Home > Hamiltonian group

Clearly, every abelian group has this property, because all subgroups of an abelian group are normal subgroups, but there are non-abelian examples as well. The most familiar (and smallest) is the quaternion group of order 8, denoted by Q₈.

It can be shown that every Hamiltonian group is a direct sum of the form G = Q₈ + B + D, where B is the direct sum of some number of copies of the cyclic group C₂, and D is a periodic abelian group with all elements of odd order.

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Topics: Hamiltonian Group Abelian Theory Order Sum Normal Subgroups...

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Hamiltonian (quantum mechanics)The Hamiltonian denoted H has two distinct but closely related meanings. In classical mechanics, it is a function that describes the state of a mechanical system in terms of position and momentum variables (i. symplectic variables), which is the basis for Hamiltonian groupIn group theory, a non-abelian group G is called Hamiltonian if every subgroup of G is normal. Clearly, every abelian group has this property, because all subgroups of an abelian group are normal subgroups, but there are non-abelian examples as well. Hamiltonian mechanicsHamiltonian mechanics is a re-formulation of classical mechanics that was invented in 1833 by William Rowan Hamilton. It arose from Lagrangian mechanics, another re-formulation of classical mechanics, introduced by Joseph Louis Lagrange in 1788. It can ho Hamiltonian pathIn graph theory, a Hamiltonian path (also called traceable path is a path that visits each vertex exactly once. A Hamiltonian cycle (also called Hamiltonian circuit vertex tour or graph cycle is a cycle that visits each vertex exactly once, except for the HamiltonianIn physics, Hamiltonian has two distinct but closely related meanings. In classical mechanics, the Hamiltonian is a function describing the state of a mechanical system in terms of position and momentum variables. See Hamiltonian mechanics. In quantum mec Hamiltonian constraintIn theories with reparametrization invariance with respect to time, if a canonical Hamiltonian formulation using first class constraints of it is possible (in general, we might have second class constraints), we'd have "gauge" "symmetries" (which really m