Group theory and generalizations Finite groups Concept
Simple group
Summary
A simple group is a nontrivial group whose only normal subgroups are the trivial subgroup and the group itself. The finite simple groups are the building blocks of all finite groups.
Where this leads
21 pages build on this one.
- Z* theorem
- Conway groups
- Suzuki groups
- Sporadic group
- Feit–Thompson theorem
- Fitting subgroup
- Hall's theorem on solvable groups
- Pariah groups
- Fischer groups
- Monster group
- Hall subgroup
- Monstrous moonshine
- Krohn–Rhodes theory
- Multiply transitive group action
- Brauer–Fowler theorem
- Janko groups
- Mathieu groups
- Baby Monster group
- Tits group
- Ree groups
- O'Nan–Scott theorem
Further reading
- Web https://en.wikipedia.org/wiki/Simple_group, lead section
About this page
| Tag | 0YMYMNQ0QZ |
|---|---|
| URI | m2://0YMYMNQ0QZ |
| Kind | concept |
| Writing | W1 stated |
| MSC | 20E32 |
| Specializes | Group |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (1 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Definitions
Used by
- Z* theorem
- Conway groups
- Suzuki groups
- Sporadic group
- Feit–Thompson theorem
- Fitting subgroup
- Hall's theorem on solvable groups
- Fischer groups
- Monster group
- Krohn–Rhodes theory
- Brauer–Fowler theorem
- Janko groups
- Mathieu groups
- Baby Monster group
- Tits group
- Ree groups
- O'Nan–Scott theorem