# All finite solvable groups satisfy the Taketa inequality

## TL;DR

This paper proves that every finite solvable group meets the Taketa inequality, linking the derived length to the number of distinct irreducible character degrees, confirming the Isaacs-Seitz conjecture.

## Contribution

It establishes that all finite solvable groups satisfy the Isaacs-Seitz conjecture, a significant step in understanding their character theory.

## Key findings

- Proves the Isaacs-Seitz conjecture for all finite solvable groups.
- Shows the derived length is bounded by the number of distinct irreducible character degrees.
- Confirms a long-standing conjecture in group theory.

## Abstract

In this paper, we prove that all finite solvable groups satisfy the Isaacs-Seitz conjecture namely the derived lenght of a finite solvable group G is less than or equal to the number of distinct irreducible complex character degrees of G.

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Source: https://tomesphere.com/paper/1704.06858