Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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A NOTE ON PRIMITIVE SUBGROUPS OF FINITE SOLVABLE GROUPS

  • He, Xuanli (Department of Mathematics Guangxi University) ;
  • Qiao, Shouhong (School of Applied Mathematics Guangdong University of Technology) ;
  • Wang, Yanming (Lingnan College and Department of Mathematics Sun Yat-sen University)
  • Received : 2012.02.07
  • Published : 2013.01.31
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Abstract

In [5], Johnson introduced the primitivity of subgroups and proved that a finite group G is supersolvable if every primitive subgroup of G has a prime power index in G. In that paper, he also posed an interesting problem: what a group looks like if all of its primitive subgroups are maximal. In this note, we give the detail structure of such groups in solvable case. Finally, we use the primitivity of some subgroups to characterize T-group and the solvable $PST_0$-groups.

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References

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Cited by

  1. PRIMITIVE SUBGROUPS AND PST-GROUPS vol.89, pp.03, 2014, https://doi.org/10.1017/S0004972713000592
  2. Some subgroup embeddings in finite groups: A mini review vol.6, pp.3, 2015, https://doi.org/10.1016/j.jare.2014.04.004