Abstract
We say that a finite group \(G\) is a DAED-group (i.e., a group with divisibility among even degrees) if for any \(1<a<b\) in the set of even degrees of the complex irreducible characters of \(G, a\) divides \(b\). In this note, we show that any DAED-group has precisely one nonabelian chief factor. Furthermore, we show that the factor is isomorphic to \(L_2(2^f)\) for some \(f\ge 2\). Our motivation comes from a problem raised by Kazarin and Berkovich in their paper “On Thompson’s theorem”, which asked about the structure of the finite nonsolvable DAED-groups.
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The author would like to thank the reviewers for their valuable comments and corrections.
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Communicated by J. S. Wilson.
Supported by Anhui provincial colleges and universities’ outstanding young talent fund project 2011SQL100.
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Yang, X. Divisibility among even character degrees. Monatsh Math 178, 645–651 (2015). https://doi.org/10.1007/s00605-014-0710-7
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DOI: https://doi.org/10.1007/s00605-014-0710-7