A group is called minimal non-abelian if it is non-abelian and all proper subgroups are abelian.


Does this notion also exist with Lie groups or algebras? As an example, consider the Lie algebra defined by the generators $\{e\_1,e\_2\}, [e\_1,e\_2]=e\_2$. Do you have a paper at hand?



Minimal non-abelian groups -> Lie groups/algebras
These Lie algebras were called *semiabelian* by some authors. Some old papers are [On the structure of simple-semiabelian
Lie-algebras](https://projecteuclid.org/journals/pacific-journal-of-mathematics/volume-111/issue-2/On-the-structure-of-simple-semiabelian-Lie-algebras/pjm/1102710571.pdf) by Farnsteiner and [On simple semiabelian $p$-adic lie algebras](https://www.tandfonline.com/doi/pdf/10.1080/00927879208824390) by myself.


