The composition factors of the 2-biset functor of kernel of the monomial linearization map

In this thesis, we find the composition factors of the 2-biset functor of kernel of the monomial linearization map. We prove that it is equivalent to finding the composition factors of $\mathbb{C}^{*}$-fibered 2-biset functor $S_{C_{2},1,1,1}$ as a 2-biset functor over $\mathbb{C}$. We show that there is no composition factor of the form $S_{H,V}$ unless $H$ is a cyclic group or $C_{2} \times C_{2^{m}}$. Moreover, we classify all composition factors of the form $S_{C_{2^{m}},V}$.