Are all finite groups Lie groups?Which Algebraic Properties Distinguish Lie Groups from Abstract Groups?Why are Lie Groups so “rigid”?Lie Groups of bigger cardinalityLie groups and Lie algebras for matricesAre there nonsmooth Lie groups?Why is the number of components of Lie group finite?Analogies between finite groups and Lie groupsAre all Lie groups Matrix Lie groups?Groups have the same Lie algebraGroups which are not Lie groups
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Are all finite groups Lie groups?
Which Algebraic Properties Distinguish Lie Groups from Abstract Groups?Why are Lie Groups so “rigid”?Lie Groups of bigger cardinalityLie groups and Lie algebras for matricesAre there nonsmooth Lie groups?Why is the number of components of Lie group finite?Analogies between finite groups and Lie groupsAre all Lie groups Matrix Lie groups?Groups have the same Lie algebraGroups which are not Lie groups
$begingroup$
Is it possible to find an isomorphism from any finite group to a Lie group (which has manifold dimension 0 and equipped with the discrete topology)?
group-theory differential-geometry finite-groups lie-groups
edited Mar 22 at 15:39
José Carlos Santos
173k23133241
asked Mar 22 at 15:33
zornzorn
516
$endgroup$
add a comment |
$begingroup$
Is it possible to find an isomorphism from any finite group to a Lie group (which has manifold dimension 0 and equipped with the discrete topology)?
group-theory differential-geometry finite-groups lie-groups
edited Mar 22 at 15:39
José Carlos Santos
173k23133241
asked Mar 22 at 15:33
zornzorn
516
$endgroup$
add a comment |
$begingroup$
Is it possible to find an isomorphism from any finite group to a Lie group (which has manifold dimension 0 and equipped with the discrete topology)?
group-theory differential-geometry finite-groups lie-groups
edited Mar 22 at 15:39
José Carlos Santos
173k23133241
asked Mar 22 at 15:33
zornzorn
516
$endgroup$
Is it possible to find an isomorphism from any finite group to a Lie group (which has manifold dimension 0 and equipped with the discrete topology)?
group-theory differential-geometry finite-groups lie-groups
group-theory differential-geometry finite-groups lie-groups
edited Mar 22 at 15:39
José Carlos Santos
173k23133241
asked Mar 22 at 15:33
zornzorn
516
edited Mar 22 at 15:39
José Carlos Santos
173k23133241
asked Mar 22 at 15:33
zornzorn
516
edited Mar 22 at 15:39
José Carlos Santos
173k23133241
edited Mar 22 at 15:39
José Carlos Santos
173k23133241
edited Mar 22 at 15:39
José Carlos Santos
173k23133241
173k23133241
asked Mar 22 at 15:33
zornzorn
516
asked Mar 22 at 15:33
zornzorn
516
asked Mar 22 at 15:33
zornzorn
516
516
add a comment |
add a comment |
1 Answer
1
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votes
$begingroup$
Yes, if you see a finite group as a $0$-dimensional manifold, then it is automatically a Lie group. And I will tell you more: it will be a compact Lie group!
answered Mar 22 at 15:34
José Carlos SantosJosé Carlos Santos
173k23133241
$endgroup$
add a comment |
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1 Answer
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1 Answer
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$begingroup$
Yes, if you see a finite group as a $0$-dimensional manifold, then it is automatically a Lie group. And I will tell you more: it will be a compact Lie group!
answered Mar 22 at 15:34
José Carlos SantosJosé Carlos Santos
173k23133241
$endgroup$
add a comment |
$begingroup$
Yes, if you see a finite group as a $0$-dimensional manifold, then it is automatically a Lie group. And I will tell you more: it will be a compact Lie group!
answered Mar 22 at 15:34
José Carlos SantosJosé Carlos Santos
173k23133241
$endgroup$
add a comment |
$begingroup$
Yes, if you see a finite group as a $0$-dimensional manifold, then it is automatically a Lie group. And I will tell you more: it will be a compact Lie group!
answered Mar 22 at 15:34
José Carlos SantosJosé Carlos Santos
173k23133241
$endgroup$
Yes, if you see a finite group as a $0$-dimensional manifold, then it is automatically a Lie group. And I will tell you more: it will be a compact Lie group!
answered Mar 22 at 15:34
José Carlos SantosJosé Carlos Santos
173k23133241
answered Mar 22 at 15:34
José Carlos SantosJosé Carlos Santos
173k23133241
answered Mar 22 at 15:34
José Carlos SantosJosé Carlos Santos
173k23133241
answered Mar 22 at 15:34
José Carlos SantosJosé Carlos Santos
173k23133241
173k23133241
add a comment |
add a comment |
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