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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Derived lengths and character degrees


Author: Mark L. Lewis
Journal: Proc. Amer. Math. Soc. 126 (1998), 1915-1921
MSC (1991): Primary 20C15
MathSciNet review: 1452810
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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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Additional Information

Mark L. Lewis
Affiliation: Department of Mathematics and Computer Science, Kent State University, Kent, Ohio 44242
Email: lewis@mcs.kent.edu

DOI: https://doi.org/10.1090/S0002-9939-98-04391-3
Received by editor(s): December 16, 1996
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1998 American Mathematical Society