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Some open questions in the theory of generalized permutable subgroups

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Abstract

A subgroup H of a group G is said to be weakly s-supplemented in G if H has a supplement T in G such that H ∩ T ⩽ H sG , where H sG is the largest s-permutable subgroup of G contained in H. This paper constructs an example to show that the open questions 6.3 and 6.4 in J Algebra, 315: 192–209 (2007) have negative solutions, and shows that in many cases Question 6.4 is positive. A series of known results are unified and generalized.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xuzhou Normal University, Xuzhou, 221116, China

    WenBin Guo & FengYan Xie

  2. School of Mathematics, Chengdu University of Information Technology, Chengdu, 610225, China

    BaoJun Li

Authors
  1. WenBin Guo
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  2. FengYan Xie
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  3. BaoJun Li
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Correspondence to WenBin Guo.

Additional information

This work was supported by National Natural Science Foundation of China (Grant No. 10771180)

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Guo, W., Xie, F. & Li, B. Some open questions in the theory of generalized permutable subgroups. Sci. China Ser. A-Math. 52, 2132–2144 (2009). https://doi.org/10.1007/s11425-009-0045-3

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  • DOI: https://doi.org/10.1007/s11425-009-0045-3

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