- #1

Mr Davis 97

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## Homework Statement

Let ##G## be any group. Recall that the center of ##G##, or ##Z(G)## is ##\{ x \in G ~ | ~ xg =

gx, ~ \forall g \in G\}##. Show that ##G / Z(G)## is isomorphic to ##Inn(G)##, the group of inner automorphisms of ##G## by ##g##.

## Homework Equations

## The Attempt at a Solution

I am not sure where to get started. I know that I am trying to find a particular isomorphism, but not sure how to find what that isomorphism must be, or whether that map will go from ##G / Z(G)## to ##Inn(G)## or the other way around.