The construction of nuclei for normal constituents of Bπ-characters

Abstract

Let GG be a π\pi -separable group for some set π\pi of primes, let χ∈Bπ(G)\chi \in {B}_{\pi }\left(G) and let N◃GN\hspace{0.33em}\triangleleft \hspace{0.33em}G. In this article, we explore how to construct a nucleus for an irreducible constituent of χN{\chi }_{N} via the given nucleus (W,γ)\left(W,\gamma ) for χ\chi .

Keywords

• π-separable group
• nucleus
• fong character
• quasi-primitive character
• 20c15
• 20c20