Induction of Characters and Finite $p$-Groups

Details Induction of Characters and Finite $p$-Groups Induction of Characters and Finite $p$-Groups

2005-07-16

arxiv.org/abs/math/0507335v2

Mathematics

Group Theory

11 pages, corrected typos

Scientific paper

Let $G$ be a finite $p$-group, where $p$ is an odd prime number,
$H$ be a subgroup of $G$ and $\theta\in \Irr(H)$ be an irreducible character
of $H$. Assume also that $|G:H|=p^2$. Then the character $\theta^G$ of $ G$
induced by $\theta$ is either a multiple of an irreducible character of $G$, or
has at least $\frac{p+1}{2}$ distinct irreducible constituents.

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