Rank of Unit Group of Burnside Ring: Final Function

We spent the seventh week on coding for the final function. The coding process was very exhausting but Dr. Carman and I were so excited and happy to see our final function that can return the correct output (rank of unit group of B(G)) for an input group. After testing the function on different groups, we found that the the final function works for groups as large as S9 and M22, which is a much better result comparing to the first version which stopped working for S3.

Below is the final code with explanation of the purpose of each step.BurnsideUnits copy

With the efficient program for calculating the size of unit group of B(G) developed during the last week, we were able to calculate sizes for a large amount of groups with different properties and observe their patterns. Function examples