ABSTRACT
Preview Activity 28.1. If we have two integers, say k and m, we can combine these integers in different ways (e.g., using addition or multiplication) to obtain another integer. In a similar manner,
if we have two groups G and H , we can combine them together to make another group, called the direct product ofG andH , that contains copies of bothG andH as subgroups. We will soon define direct products formally, but before doing so, let’s take a look at an example. An operation table for
the direct product of Z2 and Z3, denoted Z2 ⊕ Z3, is shown in Table 28.1. We use the notation [a]n to indicate the congruence class of a in Zn.
