
#1
Oct1111, 09:38 PM

P: 81

1. The problem statement, all variables and given/known data
Let G be a group. Show that G/Z(G) [itex]\cong[/itex] Inn(G) 3. The attempt at a solution G/Z(G) = g^{n}Z(G) for some g ε G and for any n ε N choose some g^{1} such that g(g^{1}h) = g(hg^{1}) and the same can be done switching the g and g^{1} This doesn't feel right at all... 



#2
Oct1111, 10:10 PM

Mentor
P: 16,698

Can you find a surjective homomorphism [tex]f:G\rightarrow Inn(G)[/tex] and then apply the first isomorphism theorem? 



#3
Oct1111, 10:18 PM

Sci Advisor
HW Helper
Thanks
P: 25,175




Register to reply 
Related Discussions  
Group Theory Question involving nonabelian simple groups and cyclic groups  Calculus & Beyond Homework  1  
Automorphisms of Finite Groups  Linear & Abstract Algebra  5  
Automorphisms and some maps that are bijective  Linear & Abstract Algebra  2  
automorphisms  Calculus & Beyond Homework  6  
More automorphisms  Linear & Abstract Algebra  2 