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Paper   IPM / M / 16883
School of Mathematics
  Title:   On the average degree of some irreducible characters of a finite group
  Author(s):  Zeinab Akhlaghi
  Status:   To Appear
  Journal: Math. Nachr.
  Supported by:  IPM
  Abstract:
Let 𝐺 be a finite group and 𝑁 be a non-trivial normal subgroup of 𝐺, such that the average degree of irreducible characters in Irr.𝐺 - 𝑁/ is less than or equal to 16∕5. Then we prove that 𝑁 is solvable. Also, we prove the solvability of 𝐺, by assuming that the average degree of irreducible characters in Irr.𝐺 - 𝑁/ is strictly less than 16∕5. We show that the bounds are sharp.

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