Solve the programming task below in a Python markdown code block.
An isogram is a word that has no repeating letters, consecutive or non-consecutive. Implement a function that determines whether a string that contains only letters is an isogram. Assume the empty string is an isogram. Ignore letter case.

```python
is_isogram("Dermatoglyphics" ) == true
is_isogram("aba" ) == false
is_isogram("moOse" ) == false # -- ignore letter case
```
```C
is_isogram("Dermatoglyphics" ) == true;
is_isogram("aba" ) == false;
is_isogram("moOse" ) == false; // -- ignore letter case
```
Also feel free to reuse/extend the following starter code:
```python
def is_isogram(string):
```