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Reading Questions 3.4 Reading Questions

1.

In the group \(\mathbb Z_8\) compute, (a) \(6+7\text{,}\) and (b) \(2^{-1}\text{.}\)

2.

In the group \(U(16)\) compute, (a) \(5\cdot 7\text{,}\) and (b) \(3^{-1}\text{.}\)

3.

State the definition of a group.

4.

Explain a single method that will decide if a subset of a group is itself a subgroup.

5.

Explain the origin of the term “abelian” for a commutative group.

6.

Give an example of a group you have seen in your previous mathematical experience, but that is not an example in this chapter.