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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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