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INDUCTION OF CHARACTERS AND FINITE $p$-GROUPS

Published online by Cambridge University Press:  06 December 2006

EDITH ADAN-BANTE
EDITH ADAN-BANTE
Affiliation:
University of Southern Mississippi Gulf Coast, 730 East Beach Boulevard, Long Beach MS 39560 e-mail: Edith.Bante@usm.edu
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Abstract

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Let $G$ be a finite $p$-group, where $p$ is an odd prime number, $H$ a subgroup of $G$ and s$\theta\in \hbox{\rm Irr}(H)$ 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.

Keywords

20C15
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 48 , Issue 3 , September 2006 , pp. 491 - 502
Copyright
2006 Glasgow Mathematical Journal Trust