# Homework Help: Group theory convention

1. Oct 23, 2011

### chinye11

1. The problem statement, all variables and given/known data
I've just started to study group theory, and i keep encountering questions where no operators are specified so i was wondering if there was a conventional operator that was meant to be used. For instance I had a question to prove that a cyclic group of order 14 is isomorphic with Z mod 14. This is true under addition but not under multiplication so should i presume that Z14 with unspecified operator is addition?

2. Relevant equations
None.

3. The attempt at a solution

2. Oct 23, 2011

### I like Serena

Welcome to PF, chinye11!

Z/14Z is not a group under multiplication.
(Why not?)

So it has to be addition.
As a bonus it is isomorphic to C14 (also written as Z14).

3. Oct 23, 2011

### chinye11

Z/14 is not a group under multiplication because not every element has an inverse, my bad didn't check it.

4. Oct 23, 2011

### I like Serena

Yep!

The group Z mod 14 with multiplication is denoted as (Z/14Z)x or as (Z/14Z)*.
That is, the same set, but with all elements that do not have an inverse removed.