by Cox, Anton

We show how the tilting tensor product theorem for algebraic groups implies a reduction formula for decomposition numbers of the symmetric group. We use this to prove generalisations of various theorems of Erdmann and of James and Williams.

DOI: 10.1007/s10468-007-9051-8
Online Date: 3/27/2007
Print publication date: 8/1/2007
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by Moretó, Alexander

Given a group G, Γ(G) is the graph whose vertices are the primes that divide the degree of some irreducible character and two vertices p and q are joined by an edge if pq divides the degree of some irreducible character of G. By a definition of Lewis, a graph Γ has bounded Fitting height if the Fitting height of any solvable group G with Γ(G)=Γ is bounded (in terms of Γ). In this note, we prove that there exists a universal constant C such that if Γ has bounded Fitting height and Γ(G)=Γ then h(G)≤C. This solves a problem raised by Lewis.

DOI: 10.1007/s10468-007-9047-4
Online Date: 3/23/2007
Print publication date: 8/1/2007
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