Even character degrees and normal Sylow 2-subgroups

Hongfei Pan 1 , Nguyen Ngoc Hung 2 ,  and Shuqin Dong 3
  • 1 School of Mathematical Sciences, Huaiyin Normal University, Jiangsu, 223300, Huaian, P. R. China
  • 2 Department of Mathematics, The University of Akron, OH 44325, Akron, USA
  • 3 School of Mathematical Sciences, Yangzhou University, Jiangsu, 225002, Yangzhou, P. R. China
Hongfei Pan
  • Corresponding author
  • School of Mathematical Sciences, Huaiyin Normal University, Huaian, Jiangsu, 223300, P. R. China
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, Nguyen Ngoc Hung and Shuqin Dong

Abstract

The Ito–Michler theorem on character degrees states that if a prime 𝑝 does not divide the degree of any irreducible character of a finite group 𝐺, then 𝐺 has a normal Sylow 𝑝-subgroup. We give some strengthened versions of this result for p=2 by considering linear characters and those of even degree.

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The Journal of Group Theory is devoted to the publication of original research articles in all aspects of group theory. Articles concerning applications of group theory and articles from research areas which have a significant impact on group theory will also be considered.

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