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On R-conjugate-permutability of sylow subgroups

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Abstract

A subgroup H of a finite group G is said to be conjugate-permutable if HH g = H g H for all g ∈ G. More generaly, if we limit the element g to a subgroup R of G, then we say that the subgroup H is R-conjugate-permutable. By means of the R-conjugatepermutable subgroups, we investigate the relationship between the nilpotence of G and the R-conjugate-permutability of the Sylow subgroups of A and B under the condition that G = AB, where A and B are subgroups of G. Some results known in the literature are improved and generalized in the paper.

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Authors and Affiliations

  1. Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, School of Mathematics and Information Sciences, Henan Normal University, No. 46, Jianshe East Road, Xinxiang, Henan, 453007, P.R. China

    Xianhe Zhao & Ruifang Chen

Authors
  1. Xianhe Zhao
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  2. Ruifang Chen
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Corresponding author

Correspondence to Xianhe Zhao.

Additional information

The research has been supported by the NSFC (Grant no. 11501176, U1504101, U1204101, 11471266), Fundamental Research Funds for the Central Universities (no.XDJK2014C163) and the Major Project of Education Department of Henan Province (no. 13B110085).

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Zhao, X., Chen, R. On R-conjugate-permutability of sylow subgroups. Czech Math J 66, 111–117 (2016). https://doi.org/10.1007/s10587-016-0243-4

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  • DOI: https://doi.org/10.1007/s10587-016-0243-4

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