Subgroup ↩

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created: 2021-11-05 23:59:08
modified: 2022-11-13 11:36:59

is a subgroup of the group if it forms a group itself with the operation on . (I.e. is closed for group multiplication)

Notation

Check for finite groups

If we want to check if is really a subgroup, making sure that is enough (see Operations on group subsets) because it guarantees that

Trivial subgroups

Examples

  1. For any integer , the set

is a subgroup of the group .

  1. The set of matrices in the GL group with positive determinants

    is a subgroup of the group .