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subgroup
Sign in to saveIn group theory, a branch of mathematics, a subset of a group G is a subgroup of G if the members of that subset form a group with respect to the group operation in G.
In the Vinony graph
Vinony's link graph records 721 inbound references to subgroup, and connects out to Lie group, group action and infimum and supremum.
Vinony files it under Group theory and Subgroup properties.
Vinony links it to 42 Wikipedia language editions.
Wikidata facts
- Subclass of
- coset
- Part of
- group theory
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- WikiProject Mathematics
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Encyclopedic overview
15 sectionsContents
- Subgroup tests
- Basic properties of subgroups
- Cosets and Lagrange's theorem
- Example: Subgroups of S<sub>4</sub>{{anchor|Subgroups of S4}}
- 24 elements
- 12 elements
- 8 elements
- 6 elements
- 4 elements
- 3 elements
- 2 elements
- 1 element
- Other examples
- Notes
- References
In group theory, a branch of mathematics, a subset of a group G is a subgroup of G if the members of that subset form a group with respect to the group operation in G.
Formally, given a group under a binary operation ∗, a subset of is called a subgroup of if also forms a group under the operation ∗. More precisely, is a subgroup of if the restriction of ∗ to is a group operation on . This is often denoted , read as " is a subgroup of ".
Excerpted from Wikipedia’s “subgroup” article, available under the CC BY-SA 4.0 licence.