Rank of Unit Group of Burnside Ring: Linear character and Elementary Abelian 2 Groups

The work of Week 5 led to some new results that would improve the efficiency of original function and gave me the confidence about the direction of my work. However, finding all the normalizers of index 2 subgroups is still a very computationally heavy process in GAP. After doing a lot of literature review and talking to Dr. Carman, I think linear character and elementary abelian 2 group can be the breakthrough.

     Through programming in GAP and reading and analyzing relevant sources such as books and papers, I was able to gain a deeper understanding of the Mathematical meaning of the size of the unit group of B(G). The goal of Week 6 is to optimize the process of finding all the unit group less computationally expensive.

 

Linear Character Copy 2

I spent the later half of the sixth week on proving the above statements to build a solid foundation for the coding part. The proofs are shown in the graph below.

proofs

After proving the propositions, I now have a clearer idea of how to substitute equivalent statements to minimize the running time in GAP. I will convert the thoughts into GAP codes next week!