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 $|\operatorname {cd}(G)|-n+1$.References
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Additional Information
- Mark L. Lewis
- Affiliation: Department of Mathematics and Computer Science, Kent State University, Kent, Ohio 44242
- MR Author ID: 363107
- Email: lewis@mcs.kent.edu
- Received by editor(s): December 16, 1996
- Communicated by: Ronald M. Solomon
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 1915-1921
- MSC (1991): Primary 20C15
- DOI: https://doi.org/10.1090/S0002-9939-98-04391-3
- MathSciNet review: 1452810