Extending Characters from Hall Subgroups

Suppose that $G$ is a finite $\pi$-separable group. A classical result asserts that all irreducible characters of a Hall $\pi$-subgroup $H$ of $G$ extend to $G$ if and only if $H$ has a normal complement in $G$. Now, we fix a prime $p$ and analyze when only the $p'$-degree irreducible characters of $H$ extend to $G$.

2010 Mathematics Subject Classification: 20C15 (primary), 20G40 (secondary)

Keywords and Phrases: extensions of characters, Hall subgroups, Sylow normalizers, $\pi$-separable groups

Full text: dvi.gz 43 k, dvi 101 k, ps.gz 349 k, pdf 229 k.

Home Page of DOCUMENTA MATHEMATICA