Exploring the Associated Groups of Quasi-Free Groups
DOI:
https://doi.org/10.29020/nybg.ejpam.v17i3.5258Keywords:
Free groups, cyclic groups, quasi-free group, free product of groups and associated groups.Abstract
If G is a cyclic group, then H (G) is a trivial group and if G= G1*...*Gn is the free product of the groups G1,..., Gn, then H(G)= H(G1*...*Gn) isomorphic of H (G1)*...*H(Gn). Furthermore, if the groups G1, G2,..., Gn are cyclic groups, then H(G) is a trivial group. In this paper we show that for every group G there exists a group denoted H (G) and is called the associated group of G satisfying some important properties that as application we show that if F is a quasi-free group and G is any group, then F(H) is trivial and H(F*G) isomorphic H(G), where a group is termed a quasi-free group if it is a free product of cyclic groups of any order.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 European Journal of Pure and Applied Mathematics
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.
By agreeing to this statement, you acknowledge that:
- You retain full copyright over your work.
- The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
- This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.