My Math Forum Help with a problem of isomorphisms.
 User Name Remember Me? Password

 Abstract Algebra Abstract Algebra Math Forum

 November 11th, 2014, 05:32 PM #1 Newbie   Joined: Feb 2014 Posts: 6 Thanks: 1 Help with a problem of isomorphisms. Let $H\leq G$ and are $N(H)$, $C(H)$ and $I(H)$ the normalizer of $H$, the centralizer of $H$ and the group of all inner automorphisms of $H$, respectively. Show that $N(H)/C(H)\cong I(H)$. Last edited by robinhg; November 11th, 2014 at 05:34 PM.
 January 26th, 2015, 07:59 AM #2 Senior Member     Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 156 Math Focus: Abstract algebra Let $\phi_g\in\mathrm I(G)$ be the inner automorphism induced by $g\in G$ i.e. $\phi_g(x)=gxg^{-1}$ for all $x\in G$. Now define $f:\mathrm N(H)\to\mathrm I(H)$ by $f(n)=\phi_n$ for $n\in\mathrm N(H)$ (check that this definition makes sense) and show that $f$ is a surjective homomorphism with kernel $\mathrm C(H)$.

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Artus Abstract Algebra 4 January 2nd, 2013 10:36 AM Kappie Abstract Algebra 3 March 1st, 2012 01:11 PM Hyperreal_Logic Applied Math 2 January 27th, 2010 07:25 AM riemannsph12 Abstract Algebra 0 November 13th, 2008 02:11 PM Jamers328 Abstract Algebra 5 November 6th, 2008 08:21 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top