Finite Nilpotent Groups Whose Cyclic Subgroups are TI-Subgroups

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Abstract

A subgroup H of a group G is called a TI-subgroup if \(H^g\cap H=1\) or H for all \(g\in G\); and H is called quasi TI if \(\mathcal {C}_G(x)\le \mathcal {N}_G(H)\) for all non-trivial elements \(x\in H\). A group G is called (quasi CTI-group) CTI-group if every cyclic subgroup of G is a (quasi TI-subgroup) TI-subgroup. It is clear that TI subgroups are quasi TI. We first show that finite nilpotent quasi CTI-groups are CTI. In this paper, we classify all finite nilpotent CTI-groups.

Keywords

TI-group CTI-groups p-Group 

Mathematics Subject Classification

20D60 

Notes

Acknowledgments

The research of the first author was in part supported by a Grant (No. 93050219) from School of Mathematics, Institute for Research in Fundamental Sciences (IPM). The research of the first author is also financially supported by the Center of Excellence for Mathematics, University of Isfahan.

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Copyright information

© Malaysian Mathematical Sciences Society and Universiti Sains Malaysia 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IsfahanIsfahanIran
  2. 2.School of MathematicsInstitute for Research in Fundamental Sciences (IPM)TehranIran
  3. 3.Department of MathematicsUniversity of TabrizTabrizIran

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