Finite Minimal Simple Groups Non-satisfying the Basis Property
DOI:
https://doi.org/10.29020/nybg.ejpam.v16i3.4871Keywords:
Simple group, Minimal group, Group with the Basis PropertyAbstract
Let G be a finite group. We say that G has the Basis Property if every subgroup H of G has a minimal generating set (basis), and any two bases of H have the same cardinality. A group G is called minimal not satisfying the Basis Property if it does not satisfy the Basis Property, but all its proper subgroups satisfy the Basis Property. We prove that the following groups PSL(2, 5) ∼A5, PSL(2, 8) , are minimal groups non satisfying the Basis Property, but the groups PSL(2, 9), PSL(2, 17) and PSL(3, 4) are not minimal and not satisfying the Basis Property.
Downloads
Published
Issue
Section
License
Copyright (c) 2023 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.