Tuesday, 17 January 2017

abstract algebra - Subgroup of multiplicative group of nonzero real numbers BbbR with index 2




Let R denote the multiplicative group of nonzero real numbers. Is there a subgroup of R with index 2?


Answer



Show that the signum function sgn is a homomorphism from R onto the multiplicative group {1,1}. The kernel of this homomorphism has index 2.


No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find limh0sin(ha)h without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...