Chemical element cubic centimeter (g/cm). Since several elements are gases at commonly encountered temperatures, their densities are usually stated for their gaseous forms; when liquefied or solidified, the gaseous elements have densities similar to those of the other elements. When an element has allotropes with different densities, one representative allotrope is typically selected in summary presentations, while densities for each allotrope can be stated where more detail is provided. For example, the three familiar allotropes of carbon (amorphous carbon, graphite, and diamond) have densities of 1.8–2.1, 2.267, and 3.515 g/cm, respectively. The elements studied to date as solid samples have eight kinds
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