ScholarLens Back to search
2019•Communications in AlgebraRequires access

Isaacs–Seitz conjecture for certain groups

Sajjad Mahmood Robati

Open publisher page 1 citations

Abstract

Let G be a finite group. I. M. Isaacs and G. Seitz have conjectured that if G is a solvable group, then Taketa’s inequality dl(G)≤|cd(G)| holds, where cd(G) is the set of irreducible character degrees of G and dl(G) is the derived length of G. In this paper, we show that this inequality holds if G is a solvable Frobenius group. Also, we prove that if dl(G/P)≤|cd(G/P)| for some normal Sylow p-subgroup P of G, then dl(G)≤|cd(G)|. Moreover, we investigate this conjecture for some sets of the real-valued irreducible character degrees.

About this research paper

What this paper is about

Let G be a finite group. I. M. Isaacs and G. Seitz have conjectured that if G is a solvable group, then Taketa’s inequality dl(G)≤|cd(G)| holds, where cd(G) is the set of irreducible character degrees of G and dl(G) is the derived length of G. In this paper, we show that this inequality holds if G is a solvable Frobenius group. Also, we prove that if dl(G/P)≤|cd(G/P)| for some normal Sylow p-subgroup P of G, then dl(G)≤|cd(G)|. Moreover, we investigate this conjecture for some sets of the real-valued irreducible character degrees.

Why it matters

OpenAlex reports 1 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Let G be a finite group. I. M. Isaacs and G. Seitz have conjectured that if G is a solvable group, then Taketa’s inequality dl(G)≤|cd(G)| holds, where cd(G) is the set of irreducible character degrees of G and dl(G) is the derived length of G. In this paper, we show that this inequality holds if G is a solvable Frobenius group. Also, we prove that if dl(G/P)≤|cd(G/P)| for some normal Sylow p-subgroup P of G, then dl(G)≤|cd(G)|. Moreover, we investigate this conjecture for some sets of the real-valued irreducible character degrees.

Key concepts: Mathematics, Sylow theorems, Conjecture, Combinatorics, Character (mathematics), Solvable group, Finite group, Group (periodic table)

Related papers

Related paper 1Related paper 2
Back to paper searchBrowse research topicsOriginal source
Isaacs–Seitz conjecture for certain groups — Research Paper | ScholarLens