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A note on 2-nilpotence of finite groups

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Abstract

Ballester-Bolinches and Guo showed that a finite group G is 2-nilpotent if G satisfies: (1) a Sylow 2-subgroup P of G is quaternion-free and (2) Ω1(P ∩  G′) ≤ Z(P) and N G (P) is 2-nilpotent. In this paper, it is obtained that G is a non-2-nilpotent group of order 16q for an odd prime q satisfying (1) a Sylow 2-subgroup P of G is not quaternion-free and (2) Ω1(P ∩ G′) ≤ Z(P) and N G (P) is 2-nilpotent if and only if q = 3 and G ≅ GL 2(3).

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References

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Acknowledgements

The first author was supported by the NSFC (Grant No. 11201401) and China Postdoctoral Science Foundation (Grant No. 201104027). The second author was supported by NSFC (Grant No. 11201403) and “Agencija za raziskovalno dejavnost Republike Slovenije”, research program P1-0285.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Yantai University, Yantai, 264005, China

    JIANGTAO SHI & CUI ZHANG

  2. University of Primorska, IAM, Muzejski trg 2, 6000, Koper, Slovenia

    CUI ZHANG

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  1. JIANGTAO SHI
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  2. CUI ZHANG
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Correspondence to CUI ZHANG.

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SHI, J., ZHANG, C. A note on 2-nilpotence of finite groups. Proc Math Sci 123, 235–238 (2013). https://doi.org/10.1007/s12044-013-0122-y

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  • DOI: https://doi.org/10.1007/s12044-013-0122-y

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