Normal Subgroup
Let 
be a subgroup
of a group 
. The similarity
transformation of 
by a fixed element 
in 
not in
always gives a subgroup.
If
 |
for every element 
in 
, then 
is said to be
a normal subgroup of 
, written 
(Arfken
1985, p. 242; Scott 1987, p. 25). Normal subgroups are also known as invariant
subgroups or self-conjugate subgroup (Arfken 1985, p. 242).
All subgroups of Abelian groups are normal (Arfken 1985, p. 242).
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Abelian group
