Linked Questions

2 votes
0 answers
131 views

Finite subgroups of compact simple Lie groups [duplicate]

The finite subgroups of $SU(2)$ consist of the symmetry groups of the Platonic solids plus the finite subgroups of $O(2)$. I would like to know if there are any results concerning $SU(3)$. In ...
Eugene Z. Xia's user avatar
10 votes
1 answer
902 views

Model theory of the complex numbers with conjugation

Do there exist some results on the theory of $\mathbb{C}$ in the language $\{0,1+, \times, \overline{\cdot}\}$, where $\overline{\cdot}$ is the conjugation map $\overline{a+ib} = a - ib$? I'm ...
user221330's user avatar
12 votes
1 answer
604 views

Which Lie groups have finitely many conjugacy classes of subgroups of fixed isomorphism type?

Let $G$ be a real Lie group. What conditions must $G$ satisfy so that the following is true: For any finite group $\Gamma$ there exist finitely many conjugacy classes of subgroups of $G$ that are ...
user505117's user avatar
11 votes
1 answer
346 views

Alternating subgroups of $\mathrm{SU}_n $

$\DeclareMathOperator\PSU{PSU}$Let $ \PSU_n $ be the projective unitary group. Let $ A_m $ be the alternating group on $ m $ letters. $ A_5 $ is a maximal closed subgroup of $ PSU_2 \cong SO_3(\mathbb{...
Ian Gershon Teixeira's user avatar
6 votes
1 answer
528 views

Finite simple groups and $ \operatorname{SU}_n $

A follow-up question to Alternating subgroups of $\mathrm{SU}_n $. $\DeclareMathOperator\PU{PU}\DeclareMathOperator\PSU{PSU}\DeclareMathOperator\PSL{PSL}$Let $ \PU_m $ be the projective unitary group, ...
Ian Gershon Teixeira's user avatar
7 votes
1 answer
505 views

The probability that two elements of a finite nonabelian simple group commute

It is mentioned in here (last paragraph of the first page) that Dixon proved the following result: the probability that two elements of a finite nonabelian simple group commute is at most $\frac{1}{12}...
user129021's user avatar
3 votes
2 answers
321 views

Finite subgroups of Spin(9)

I'm trying to classify compact manifolds $M^{16}$ with a metric which is locally conformal to a (local) metric with holonomy (included in) Spin(9)$\subset$SO(16). To do this, I would need a complete ...
Maurizio Parton's user avatar
2 votes
1 answer
275 views

Self-normalizing implies maximal for subgroup of compact Lie group

Consider the compact group $ G=\operatorname{SO}_3(\mathbb{R}) $. The closed subgroups of $ G $ (other than the trivial group 1 and the whole group $ G $) are exactly $ O_2$, $\operatorname{SO}_2 $ ...
Ian Gershon Teixeira's user avatar
3 votes
0 answers
104 views

Where can I learn about the discrete symmetries of the complex projective plane (or space)?

I understand that $CP^1$ is the Riemann Sphere. I guess all its discrete symmetries were known for a long time and well-classified. (But suggestions or good references where this is worked out in a ...
guest78's user avatar
  • 31
4 votes
0 answers
69 views

The number of uniformly finite subgroups of some Lie groups

Let $G$ be the group $SO(n)$, $SU(n)$ or $Sp(n)$. Let $F_m$ be the collection of finite subgroups of $G$ such that its order is bounded by $m$. Two elements in $F_m$ are identified if they are ...
Totoro's user avatar
  • 2,515