Derived lengths and character degrees

Lewis, Mark

doi:10.1090/S0002-9939-98-04391-3

Derived lengths and character degrees
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by Mark L. Lewis PDF

Proc. Amer. Math. Soc. 126 (1998), 1915-1921 Request permission

Abstract:

Let $G$ be a finite solvable group. Assume that the degree graph of $G$ has exactly two connected components that do not contain $1$. Suppose that one of these connected components contains the subset $\{ a_{1}, \dots , a_{n} \}$, where $a_{i}$ and $a_{j}$ are coprime when $i \not = j$. Then the derived length of $G$ is less than or equal to $|\operatorname {cd}(G)|-n+1$.

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