- #1
mnb96
- 715
- 5
Hi,
the abelianization of a group G is given by the quotient G/[G,G], where [G,G] is the commutator subgroup of G. When dealing with finite groups, the commutator subgroup is given by the (normal) subgroup generated by all the commutators of G.
If we consider instead the case of G being a Lie group, how do we abelianize it? In particular, do we define the commutator subgroup of a Lie group G in the standard way, as all the elements of G obtained by finite sequences of commutators and their inverses?
Thanks.
the abelianization of a group G is given by the quotient G/[G,G], where [G,G] is the commutator subgroup of G. When dealing with finite groups, the commutator subgroup is given by the (normal) subgroup generated by all the commutators of G.
If we consider instead the case of G being a Lie group, how do we abelianize it? In particular, do we define the commutator subgroup of a Lie group G in the standard way, as all the elements of G obtained by finite sequences of commutators and their inverses?
Thanks.