## “School of Mathematics”

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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 ðº be a finite group and ð be a non-trivial normal subgroup of ðº, such that the average degree of irreducible characters in Irr.ðº - ð/ is less than or equal to 16â5. Then we prove that ð is solvable. Also, we prove the solvability of ðº, by assuming that the average degree of irreducible characters in Irr.ðº - ð/ is strictly less than 16â5. We show that the bounds are sharp.