Abstract
Let G be a finite group. An x∈G is a real element if x and x −1 are conjugate in G. For x∈G, the conjugacy class x G is said to be a real conjugacy class if every element of x G is real. We show that if 4 divides no real conjugacy class sizes of a finite group G, then G is solvable. We also study the structure of such groups in detail. This generalizes several results in the literature.
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