Subgroup
A subgroup is a subset 
of group
elements of a group 
that satisfies the four group
requirements. It must therefore contain the identity
element. "
is a subgroup of 
" is written
, or sometimes 
(e.g., Scott
1987, p. 16).
The order of any subgroup of a group of order 
must be a divisor
of 
.
A subgroup 
of a group 
that does not
include the entire group 
itself is known as a proper
subgroup, denoted 
or 
.
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Abelian group
