0
votes
1answer
68 views

Is there a Relationship between Quantum Groups and Lie Groups?

I know that the Lie Group is all about continuous transformation groups. I know that the quantum group denotes various kinds of noncommutative algebra with additional structure. Transformation group ...
0
votes
1answer
24 views

Find an abelian subgroup of $GL(2n, q)$ of special order

I want to prove that $GL(2n, q)$ where $q$ is even, has an abelian subgroup of order $q^{2n - 1}$. please help me.
5
votes
2answers
214 views

Subgroups of $\Bbb{R}^n$ that are closed and discrete

I am trying to prove that every closed discrete subgroup of $\Bbb{R}^n$ under addition is a free abelian group of finite rank. I have tried to do this by induction on the dimension $n$. Base ...
5
votes
1answer
368 views

Subgroups of a vector space

I would like to have an overview of how a subgroup of a vector space over $\mathbb R$ of dimension $n$ can look like. Is there a complete classification available? I know that there are for examples ...