I have 2 groups:
- general linear $ k \times k $ with $\cdot$
- top-triangle matrix $ n \times n $ with 1 on main diagonal. Operation is $\cdot$ too
Is there isomorphism for any any non-trivial $n,k$ i.e $n \neq 2 \ or \ k \neq 1$ over $\mathbb{R}$ or $\mathbb{Q}$?
If no, how can I prove it?