GAP:InnerAutomorphismsAutomorphismGroup

This article is about a GAP function.

Definition

Function type

This function takes as input a group and outputs a group.

Behavior

Nature of input	Output
A group $G$ that has previously been defined as the automorphism group of a group $K$	the subgroup of $G$ comprising the inner automorphisms of $K$ , with Parent attribute set to $G$
A group $G$ that has not been previously defined as an automorphism group	A NoMethodFound error.

Related functions

AutomorphismGroup

Examples of usage

gap> G := DihedralGroup(16);
<pc group of size 16 with 4 generators>
gap> H := AutomorphismGroup(G);
<group of size 32 with 5 generators>
gap> I := InnerAutomorphismsAutomorphismGroup(H);
<group with 3 generators>
gap> Parent(I) = H;
true
gap> J := InnerAutomorphismsAutomorphismGroup(G);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 2nd choice method found for `InnerAutomorphismsAutomorphismGroup' on 1 arguments called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue