Corpus ID: 235458536

On ECP-Groups

@inproceedings{Murashka2021OnE,
  title={On ECP-Groups},
  author={V. I. Murashka},
  year={2021}
}
According to T. Foguel a subgroup H of a group G is called conjugate-permutable if HH = HH for every x ∈ G. Mingyao Xu and Qinhai Zhang studied finite groups with every subgroup conjugate-permutable (ECP-groups) and asked three questions about them. We gave the answers on these questions. In particular, every group of exponent 3 is ECP-group, there exist non-regular ECP-3-groups and the class of all finite ECP-groups is neither formation nor variety. 

References

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On Conjugate-Permutable Subgroups of a Finite Group
Let G be a finite group. A subgroup H of G is called conjugate-permutable in G if HHg = HgH for any g ∈ G. A group G is called an ECP-group if every subgroup of G is conjugate-permutable in G. InExpand
Conjugate-Permutable Subgroups
w x In the proof that a quasinormal subgroup is subnormal 4 , one only needs to show that it is permutable with all of its conjugates. This leads to a new concept concerning subgroups. DEFINITION. AExpand
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