SOLUTION: Let H be a subgroup of G. Show that H is normal if and only if ghg−1 ∈ H for every g ∈ G, h ∈ H. Another way of writing this is: gHg−1 = H for every g ∈ G.

Algebra ->  Test -> SOLUTION: Let H be a subgroup of G. Show that H is normal if and only if ghg−1 ∈ H for every g ∈ G, h ∈ H. Another way of writing this is: gHg−1 = H for every g ∈ G.      Log On


   



Question 1158368: Let H be a subgroup of G. Show that H is normal if and only
if ghg−1 ∈ H for every g ∈ G, h ∈ H. Another way of writing
this is: gHg−1 = H for every g ∈ G.

Answer by ikleyn(52748) About Me  (Show Source):
You can put this solution on YOUR website!
.

It is the definition of the normal subgroup.