For all humankind
Academicsubsite
ZixuanZhang
ZixuanZhang
Ponder...

Subgroup

A subgroup of a group contains the identity, is closed under the operation, and contains inverses of its elements.

Definition 1.20 (Subgroup)

Let be a group and . If we have

  1. ,
  2. for all ,
  3. for all .

Then we say that is a subgroup of . We write .

Examples

and are subgroup examples.

Stated in