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Conjugacy Class Sizes of Elements of Prime-Power Order of Finite Groups

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Abstract

Let G be a finite group and p is a prime. The purpose of this paper is to investigate influences of the sizes of conjugacy classes of \(p^{\prime }\)-element of prime-power order of G on the structure of finite groups. We get some sufficient conditions for a finite group G to be p-nilpotent groups and supersolvable groups. Some known results are generalized.

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Acknowledgements

The author is very grateful to the referee who read the manuscript carefully and provided a lot of valuable suggestions and useful comments. It should be said that I could not have polished the final version of this paper well without his or her outstanding efforts. The paper is dedicated to Professor John Cossey for his 75th birthday.

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Authors and Affiliations

  1. Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, People’s Republic of China

    Qingjun Kong

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  1. Qingjun Kong
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Correspondence to Qingjun Kong.

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The research of the authors is supported by the National Natural Science Foundation of China (11301378).

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Kong, Q. Conjugacy Class Sizes of Elements of Prime-Power Order of Finite Groups. Bull. Iran. Math. Soc. 44, 405–408 (2018). https://doi.org/10.1007/s41980-018-0026-9

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  • DOI: https://doi.org/10.1007/s41980-018-0026-9

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