All Questions
4 questions
2
votes
1
answer
106
views
Conjugate subgroups by permutation matrices
Is the following statement true or false?
In $G=\operatorname{GL}_{n}(\textbf{C})$, two elementary abelian $2$-subgroups $X$ and $Y$ of $G$ whose generators are all diagonal matrices are conjugate if ...
- 1,321
2
votes
0
answers
48
views
Generation of $SU(n,q^2)$ by subgroups isomorphic to $SU(2,q^2)$
Throughout, let $q$ be an odd prime power. Let $GF(q^2)$ be the field with $q^2$ elements.
My question concerns the generation of the special unitary group $SU(n,q^2)$, where $n \ge 2$, by certain ...
- 21
20
votes
1
answer
408
views
Does $SL_2(K) \simeq SL_2(L)$ imply $K\simeq L$?
Let $K$ and $L$ be two fields. Assume characteristics are not 2. I can show in a quite elementary way that if the statement $SL_2(K) \simeq SL_2(L) \implies K \simeq L$ holds, then for $n \geq 2$, the ...
- 607
1
vote
1
answer
224
views
An automorphism that is not inner.
Consider the group $G=SL_3(\mathbb{C})$. I want to show that the automorphism $\phi$ of $G$ given by $\phi(x)=(x^{-1})^T$ is not inner. Probably I should do this by contradiction, i can show that if $\...
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