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p-parts of character degrees (2015)

Lewis, M. L., Navarro, G., Tiep, P. H., Tong-Viet, H. P.

Oxford University Press

In: Journal of the London Mathematical Society

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Publication Date: 2015-09-20

Description: We show that if $p$ is an odd prime and $G$ is a finite group satisfying the condition that $p^2$ divides the degree of no irreducible character of $G$ , then $|G:\mathbf {O}_p (G)|_p \le p^4,$ where $\mathbf {O}_p (G)$ is the largest normal $p$ -subgroup of $G$ , and if $P$ is a Sylow $p$ -subgroup of $G$ , then $P''$ is subnormal in $G$ . Our investigations suggest that if $p^a$ is the largest power of $p$ dividing the degrees of irreducible characters of $G$ , then $|G:\mathbf {O}_p(G)|_p$ is bounded by $p^{f(a)},$ where $f (a)$ is a function in $a$ and $P^{(a+1)}$ is subnormal in $G$ .

Print ISSN: 0024-6107

Electronic ISSN: 1469-7750

Topics: Mathematics

Published by Oxford University Press

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