Abstract
Let N be a normal subgroup of a group G. Suppose that the positive integers m > n are two longest non-central G-conjugacy class sizes of N with (m, n) = 1. The purpose of this paper is to determine the structure of N and give the N-conjugacy class sizes of the elements in N under that assumption that m is square free.
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Supported by National Natural Science Foundation of China (Grant No. 11271301) and NSFC-He’nan Joint Fund (Grant No. U1204101)
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Zhao, X.H., Qu, H.P. & Chen, G.Y. On coprime G-conjugacy class sizes in a normal subgroup. Acta. Math. Sin.-English Ser. 30, 1588–1594 (2014). https://doi.org/10.1007/s10114-014-2803-6
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DOI: https://doi.org/10.1007/s10114-014-2803-6