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🏠
/
Mathematics
/
Group Theory
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Subgroup Test
Subgroup Test
A simple criterion to determine if a subset of a group is a subgroup without verifying all group axioms.
📜
The statement of the theorem
A non-empty subset
H
H
H
of a group
G
G
G
is a subgroup if and only if for all
a
,
b
∈
H
a, b \in H
a
,
b
∈
H
,
a
b
−
1
∈
H
ab^{-1} \in H
a
b
−
1
∈
H
.
Source: Wikipedia