Task: Text Categorization
Input (English): Groups of this name are a subset of Dedekind groups, and they are generally non-abelian groups with every subgroup normal. This name also describes an NP-complete problem that asks if it is possible to construct a cycle visiting every vertex of a graph. For classical systems with forces independent of velocity, this quantity is equal to the total energy of the system. That quantity appears in several first-order differential equations in its namesake re-formulation of classical mechanics, and that quantity is related to the Lagrangian by a Legendre transform. For ten points, identify this multi-use term derived from the name of the inventor of quaternions.
Output (English): Science