Group Theory: Answers

Here, we look at the solution to the exercise set in this week’s tutorial, which introduced group theory.

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Solution:

Yes, they do form a group; let us see how they satisfy the four parts of the definition.

1. If we add two integers we get an integer as the result, therefore we have closure;
2. For integers the property of associativity holds;
3. 0 is the identity — remember this is with respect addition;
4. To find the inverse of a we just take -a as a + (-a) = 0, and 0 is the identity.

This article was written by David Butler, one of the course creators and teachers at Oxbridge Inspire. David is studying for a PhD at the Alan Turing Institute in London.

If you enjoyed this article, you might consider coming to our course in Cambridge this summer on the Mathematics behind Cryptography.