when do we considered a group to be a set
Group (mathematics) Many groups are simultaneously groups and examples of other mathematical structures. In the language of category theory, they are group objects in a category, meaning that they are objects (that is, examples of another mathematical structure) which come with transformations (called morphisms) that mimic the group axioms. For example, every group (as defined above) is also a set, so a group is a group object in the category of sets.
Group 11 element Group 11, by modern IUPAC numbering,[1] is a group of chemical elements in the periodic table, consisting of copper (Cu), silver (Ag), and gold (Au). Roentgenium (Rg) is also placed in this group in the periodic table, although no chemical experiments have yet been carried out to confirm that it behaves like the heavier homologue to gold. Group 11 is also known as the coinage metals, due to their former usage. They were most likely the first three elements discovered.[2] Copper, silver, and gold all occur naturally in elemental form.