# Group Theory innG is normal subgroup of autG [duplicate]

This question already has an answer here:

Any hints for proving that innG $\triangleleft$ autG for any group G.

where innG(Inner automorphism of G) and autG(Automorphism of G) and H $\triangleleft$ K (H is normal subgroup of K).

## marked as duplicate by Dietrich Burde abstract-algebra StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); May 2 '17 at 18:58

Suppose you have $\tau \in \text{inn}(G)$. Then there is a $g \in G$ such that $\tau(h) = ghg^{-1}$ for all $h \in G$. If $\sigma \in \text{Aut}(G)$, can you express $\sigma\tau\sigma^{-1}(h)$ as an inner automorphism (by an element related to $g$ somehow)?