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2021 On the geometric mean of character degrees of a finite group
Hung Ngoc Nguyen
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Albanian J. Math. 15(1): 3-9 (2021). DOI: 10.51286/albjm/1608313771

Abstract

Over the past decade, several interesting results on the so-called average character degree of a finite group and its connections with the group structure have been found. In this paper we introduce the geometric mean of character degrees and prove that the alternating group $\mathsf{A}_5$, which is the smallest non-solvable group, has minimal geometric mean of irreducible character degrees among all non-solvable groups.

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Hung Ngoc Nguyen. "On the geometric mean of character degrees of a finite group." Albanian J. Math. 15 (1) 3 - 9, 2021. https://doi.org/10.51286/albjm/1608313771

Information

Published: 2021
First available in Project Euclid: 26 March 2021

Digital Object Identifier: 10.51286/albjm/1608313771

Subjects:
Primary: 20C15 , 20D05 , 20D10

Keywords: character degrees , Finite group , geometric mean , Solvable group

Rights: Copyright © 2021 Research Institute of Science and Technology (RISAT)

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Vol.15 • No. 1 • 2021
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