# Non-Abelian Simple Finite Groups are Infinitely Many

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## Theorem

There exist infinitely many types of group which are non-abelian and finite.

## Proof

Follows directly from Alternating Group is Simple.

## Sources

- 1978: John S. Rose:
*A Course on Group Theory*... (previous) ... (next): $1$: Introduction to Finite Group Theory: $1.11$