<s>
In	O
mathematics	O
,	O
in	O
the	O
realm	O
of	O
group	O
theory	O
,	O
an	O
IA	B-Algorithm
automorphism	I-Algorithm
of	O
a	O
group	O
is	O
an	O
automorphism	O
that	O
acts	O
as	O
identity	O
on	O
the	O
abelianization	O
.	O
</s>
<s>
An	O
IA	B-Algorithm
automorphism	I-Algorithm
is	O
thus	O
an	O
automorphism	O
that	O
sends	O
each	O
coset	O
of	O
the	O
commutator	O
subgroup	O
to	O
itself	O
.	O
</s>
<s>
The	O
IA	B-Algorithm
automorphisms	I-Algorithm
of	O
a	O
group	O
form	O
a	O
normal	O
subgroup	O
of	O
the	O
automorphism	O
group	O
.	O
</s>
<s>
Every	O
inner	B-Algorithm
automorphism	I-Algorithm
is	O
an	O
IA	B-Algorithm
automorphism	I-Algorithm
.	O
</s>
