Question

Give an example, with justification, of a commutative subgroup of a non commutative
group.

Answer 1

Answer on Question #66440 – Math – Abstract Algebra

Question

Give an example with justification of a commutative subgroup of a non commutative group.

Solution

Let’s consider the quaternion group:

$$Q _ {8} = \{1, - 1, i, - i, j, - j, k, - k \}$$

It is non commutative because not all elements commutate (e.g., $ij = k$, but $ji = -k$).

One of its subgroup is

$$\{1, - 1, i, - i \}.$$

It is commutative because there is only one imaginary unit.

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