Resolved: "Let G be a cyclic group of order..." - Plainmath

College
Algebra
Abstract algebra

Scoopedepalj

Answered question

2022-02-28

Let G be a cyclic group of order 6. How many of its elements generate G?

Answer & Explanation

Radich606

Beginner2022-03-01Added 6 answers

For order

= 6

G_{1} = {1, a, a^{2}, a^{3}, a^{4}, a^{5}}

The order of

a^{k} is \frac{6}{d}

where

d = gcd (G, d)

.
So order of (a) and

(a^{5})

is 6.
while for the others order is less than 6.
Thus, only a and

a^{5}

generates the entire

G_{1}

.

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