Question

Classify all groups of the given order:115

Short answer

The group of order 115 is${\mathrm{\mathbb{Z}}}_{115}$.

Step-by-step solution

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 groups of order 115

Writing 115 as multiple of prime factors as:

$115=5\cdot 23$

Therefore, by referring tocorollary 9.18, we get p=23 and q=5 (both are primes).

Hence, the possible group of the given order is${{\mathbb{Z}}_p}_q={\mathbb{Z}}_{115}$