Diamond Diamond Diamond is a solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. At room temperature and pressure, another solid form of carbon known as graphite is the chemically stable form, but diamond almost never converts to it. Diamond has the highest hardness and thermal conductivity of any natural material, properties that are utilized in major industrial applications such as cutting and polishing tools. They are also the reason that diamond anvil cells can subject materials to pressures found deep in the Earth. Because the arrangement of atoms in diamond is extremely
Pure subgroup Pure subgroup In mathematics, especially in the area of algebra studying the theory of abelian groups, a pure subgroup is a generalization of direct summand. It has found many uses in abelian group theory and related areas. A subgroup formula_1 of a (typically abelian) group formula_2 is said to be pure if whenever an element of formula_1 has an formula_4 root in formula_2, it necessarily has an formula_4 root in formula_1. Formally, formula_8 is solvable in formula_2 formula_10 is solvable in formula_1. Pure subgroups are also called isolated subgroups or serving subgroups and were first investigated in Prüfer's 1923 paper