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A class of finite resistant p-groups

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Abstract

A finite p-group P is called resistant if, for any finite group G having P as a Sylow p-group, the normalizer N G (P) controls p-fusion in G. Let P be a central extension as

$$1 \to {\mathbb{Z}_{{p^m}}} \to P \to {\mathbb{Z}_p} \times \cdots {\mathbb{Z}_p} \to 1,$$

and |P′| ≤ p, m ≥ 2. The purpose of this paper is to prove that P is resistant.

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Authors and Affiliations

  1. Department of Mathematics, Hubei University, Wuhan, 430062, P. R. China

    He Guo Liu

  2. Department of Mathematics, He’nan University of Technology, Zhengzhou, 450001, P. R. China

    Yu Lei Wang

Authors
  1. He Guo Liu
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  2. Yu Lei Wang
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Corresponding author

Correspondence to He Guo Liu.

Additional information

Supported by NSFC (Grant Nos. 11371154, 11301150 and 11601121) and Natural Science Foundation of Henan Province of China (Grant Nos. 142300410134, 162300410066)

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Liu, H.G., Wang, Y.L. A class of finite resistant p-groups. Acta. Math. Sin.-English Ser. 33, 725–730 (2017). https://doi.org/10.1007/s10114-016-4016-7

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  • DOI: https://doi.org/10.1007/s10114-016-4016-7

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