Given a finite set G is closed under an associative product and that both cancellation laws hold in G,Then G must be a group.(adsbygoogle = window.adsbygoogle || []).push({});

I need to prove that G must be a group, I understand that for this

I only need to show that :

1) There exist the identity

2) There exist the inverse.

But while trying to do this problem , i am not able to understand how to use the fact that G is finite ?

**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!

# Finite group

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