Question

Classify all groups of the given order:143

Short answer

The group of order 143 is${\mathrm{\mathbb{Z}}}_{143}$.

Step-by-step solution

 Step 1: Referring to Corollary 9.18

Let G be a group of order pq, where p and q are primes such that p>q.

If$q\times (p-1)$ , then $G\cong {\mathbb{Z}}_{pq}$ .

Classifying group of order 143

Writing 143 as a multiple of prime factors:

$143=11\cdot 13$

Therefore, by referring tocorollary 9.18, we get p=13 and q=11 (both are primes).

Hence, the possible group of the given order is ${{\mathrm{\mathbb{Z}}}_{\mathrm{p}}}_{\mathrm{q}}={\mathrm{\mathbb{Z}}}_{143}$.