Properties of gyrogroups induced by groups whose central quotients being 2-Engel

Authors

JATURON WATTANAPANFollow
TEERAPONG SUKSUMRANFollow

Author ORCID Identifier

JATURON WATTANAPAN: 0009-0001-9391-5693

TEERAPONG SUKSUMRAN: 0000-0002-1239-5586

DOI

10.55730/1300-0098.3531

Abstract

A group Γ is said to be CCII if the quotient Γ/Z(Γ) is 2-Engel or, equivalently, commutator-inversion invariant, where Z(Γ) is the center of Γ. In this article, we prove algebraic and topological properties of gyrogroups that are induced by CCII groups. Then, using a classification of non-abelian groups of order n with n < 32, we determine all finite CCII groups of order less than 32.

Keywords

2-Engel group, CCII group, commutator-inversion invariant, gyrogroup, topological gyrogroup

First Page

634

Last Page

644

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

WATTANAPAN, JATURON and SUKSUMRAN, TEERAPONG (2024) "Properties of gyrogroups induced by groups whose central quotients being 2-Engel," Turkish Journal of Mathematics: Vol. 48: No. 4, Article 2. https://doi.org/10.55730/1300-0098.3531
Available at: https://journals.tubitak.gov.tr/math/vol48/iss4/2