Published January 1, 2021 | Version v1
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Monolithic characters of real groups

  • 1. Istanbul Univ, Dept Math, Fac Sci, Istanbul, Turkey
  • 2. Piri Reis Univ, Dept Marine Engn, Maritime Fac, Istanbul, Turkey

Description

In this article, we are concerned with the nonlinear primitive and monolithic characters of a finite real group. We give some criteria for determining whether or not a finite group is real by using its monolithic characters. Also, we classify all finite real groups which have at most two nonlinear monolithic characters and obtain a result for real groups with three nonlinear monolithic characters. Finally, we prove that there are not any nonlinear primitive irreducible characters of a finite solvable real group having at most five nonlinear monolithic characters.

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