OBTAINING NUCLEI FROM CHAINS OF NORMAL SUBGROUPS.

In this paper, we reexamine the foundation of Isaacs' π-theory. One of the key concepts in Isaacs' π-theory is the construction of the characters Bπ(G) for a π-separable group G. The key to determining which characters lie in Bπ(G) was the construction of a nucleus for each irreducible character χ. In this paper, we present a different way of finding a nucleus for χ which is based on a chain of normal subgroup $\mathcal{N}$. Using this nucleus, we obtain the set of characters $B_{\pi}(G:\mathcal{N})$. We investigate the properties that $B_{\pi}(G:\mathcal{N})$ has in common with Bπ(G). [ABSTRACT FROM AUTHOR]