Abstract
Let m, n > 1 be two coprime integers. In this paper, we prove that a finite solvable group is nilpotent if the set of the conjugacy class sizes of its primary and biprimary elements is {1,m, n,mn}.
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Shao, C., Jiang, Q. On conjugacy class sizes of primary and biprimary elements of a finite group. Sci. China Math. 57, 491–498 (2014). https://doi.org/10.1007/s11425-013-4666-1
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DOI: https://doi.org/10.1007/s11425-013-4666-1