Question

The number of generators of an infinite cyclic group is

• A. $1$
• B. $3$
• C. $2$
• D. Infinite

Answer 1

The correct option is C

$2$

The explanation for the correct option:

(C): $2$

Group Generators:

• A group of elements is called a set of generators $({\mathrm{g}}_1,...,{\mathrm{g}}_{\mathrm{n}})$ if the generators can produce all the elements in the group after being applied repeatedly to both themselves and each other.
• Powers of a single generator can produce cyclic groupings.
• Generators for a dihedral group are two elements that do not have the same ordering sign.

Number of Generators involved in an infinite cyclic group:

• Total $2$ generators are required in an infinite cyclic group.

Final Answer: Therefore, Option C is the correct option.