Subgroup (Mathematics)

up:: Group (Mathematics)

Given a group and a subset , then is a subgroup of if it is a group in its own right under the restricted operation . That is, is closed under the group operation. Thus, the following properties must hold:

1. Closed under operation:
2. Existence of neutral element:
3. Existence of inverse element:

One denotes as a shorthand for being a subgroup of .

Corollaries

The subgroup test can be simplified as

1. , since

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References

• Subgroup - Wikipedia