Template:Multiplicative group facts to check against

The discussion here about the multiplicative group of integers modulo n relies on some background facts from group theory.
FACTS ABOUT MULTIPLICATIVE GROUPS: Classification of natural numbers for which the multiplicative group is cyclic | Characterization of multiplicative group of integers modulo n
GENERAL FACTS ABOUT GROUPS: order of direct product is product of orders, exponent of direct product is lcm of exponents