(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let G1 and G2 be groups, let G = G1 x G2 and define the binary operation on G by

(a1,a2)(b1,b2):=(a1b1,a2b2)

Prove that this makes G into a group. Prove G is abelian iff G1 and G2 are abelian.

Hence or otherwise give examples of a non-cyclic abelian group of order 8 and a non-abelian group of order 42.

2. Relevant equations

3. The attempt at a solution

I have done the 1st part of this question and I'm just struggling with the examples. From reading around the subject I think a non-cyclic abelian group of order 8 would be Z2 x Z2 x Z2 where Z2 is the integers modulo 2 under addition. However, I don't really understand this.

Also, I'm unsure how to tackle the non-abelian group of order 42.

Thanks :)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Groups: cyclic, abelian

**Physics Forums | Science Articles, Homework Help, Discussion**