# 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

SHOWING 1-7 OF 7 REFERENCES

On Conjugate-Permutable Subgroups of a Finite Group

- Mathematics
- 2005

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. In… Expand

Conjugate-Permutable Subgroups

- Mathematics
- 1997

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. A… Expand

and E

- O’Brien, GAP package SmallGrp — The GAP Small Groups Library, v. 1.4.2 , 2020
- 2002

GAP package permut — A package to deal with permutability in finite groups

- v. 2.0.3, 2018
- 2014

GAP package SmallGrp -The GAP Small Groups Library

- 2002