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Paper   IPM / M / 17107
School of Mathematics
  Title:   On the average degree of linear and even degree characters of finite groups
  Author(s):  Zeinab Akhlaghi
  Status:   Published
  Journal: Ricerche mat.
  Year:  2023
  Pages:   DOI: 10.1007/s11587-022-00750-0
  Supported by:  IPM
Let G be a finite group and N be a non-trivial normal subgroup of G. Let Irr2(GjN) be the set of all linear and even degree characters of Irr(GjN) and by acd2(GjN) we mean the average degree of irreducible characters of Irr2(GjN). We prove that N is solvable if acd2(GjN)  5=2. Also, we prove the solvability of G by assuming acd2(GjN) < 5=2. Moreover, the bounds are sharp.

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