Abstract
Let N be a normal subgroup of a finite group G, and x an element of N. Objective that \(|x^G|=|G:C_G(x)|\), so \(|x^G|\) is called “minimal” when \(C_G(x)\) is a maximal subgroup of G. In this paper, we characterize the structure of N when \(|x^G|\) is minimal for every non-G-central element x of N.
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The research of the work was supported by the National Natural Science Foundation of China (11501176, 11901169), the project for high quality courses of postgraduate education in Henan Province, Research and practice project of higher education reform in Henan Normal University (post-graduate education, No. YJS2019JG06) and Key Laboratory of Applied Mathematics of Fujian Province University (Putian University, No. SX201902, SX201902).
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Zhao, X., Zhou, Y., Chen, R. et al. On the Normal Subgroup with Minimal G-Conjugacy Class Sizes. Mediterr. J. Math. 18, 266 (2021). https://doi.org/10.1007/s00009-021-01889-0
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DOI: https://doi.org/10.1007/s00009-021-01889-0