Products of characters and derived length

Details Products of characters and derived length Products of characters and derived length

2003-04-25

arxiv.org/abs/math/0304413v1

Mathematics

Group Theory

12 pages, to appear J. Algebra

Scientific paper

Let G be a finite solvable group and $\chi\in \Irr(G)$ be a faithful
character. We show that the derived length of G is bounded by a linear function
of the number of distinct irreducible constituents of $\chi\bar{\chi}$. We also
discuss other properties of the decomposition of $\chi\bar{\chi}$ into its
irreducible constituents.

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