Published online by Cambridge University Press: 01 August 2018
The first author [J. Brough, ‘On vanishing criteria that control finite group structure’, J. Algebra458 (2016), 207–215] has shown that for certain arithmetical results on conjugacy class sizes it is enough to consider only the vanishing conjugacy class sizes. In this paper we further weaken the conditions to consider only vanishing elements of prime power order.
The first author gratefully acknowledges financial support by the ERC Advanced Grant 291512 and the Alexander von Humboldt Fellowship for Postdoctoral Researchers. The research of the second author is supported by the National Natural Science Foundation of China (11301378).
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