Abstract
Let G be a finite group and let G* be the set of elements of primary, biprimary and triprimary orders of G. We show that suppose that the conjugacy class sizes of G* are exactly {1, p a, n, p a n} with (p, n) = 1 and a ≥ 0, then G is solvable.
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Communicated by John S. Wilson.
The research of the author is supported by the National Natural Science Foundation of China (10771132), SGRC (GZ310), the Research Grant of Shanghai University.
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Kong, Q. Conjugacy class sizes and solvability of finite groups. Monatsh Math 168, 267–271 (2012). https://doi.org/10.1007/s00605-011-0321-5
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DOI: https://doi.org/10.1007/s00605-011-0321-5