Abstract Algebra: Theory and Applications

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.