3.4: Reading Questions
In the group \(\mathbb Z_8\) compute, (a) \(6+7\text{,}\) and (b) \(2^{-1}\text{.}\)
In the group \(U(16)\) compute, (a) \(5\cdot 7\text{,}\) and (b) \(3^{-1}\text{.}\)
State the definition of a group.
Explain a single method that will decide if a subset of a group is itself a subgroup.
Explain the origin of the term “abelian” for a commutative group.
Give an example of a group you have seen in your previous mathematical experience, but that is not an example in this chapter.