Chemical element chemical bonds, they form chemical compounds. Only a minority of elements are found uncombined as relatively pure minerals. Among the more common of such native elements are copper, silver, gold, carbon (as coal, graphite, or diamonds), and sulfur. All but a few of the most inert elements, such as noble gases and noble metals, are usually found on Earth in chemically combined form, as chemical compounds. While about 32 of the chemical elements occur on Earth in native uncombined forms, most of these occur as mixtures. For example, atmospheric air is primarily a mixture of nitrogen, oxygen, and argon, and
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