Classification of finite minimal simple groups

Statement

Here is a list of all the finite minimal simple groups (up to isomorphism):

1. The projective special linear group $PSL(2,2^{p})$, where $p$ is a prime number.
2. The projective special linear group $PSL(2,3^{p})$, where $p$ is an odd prime.
3. The projective special linear group $PSL(2,p)$, where $p>3$ is a prime such that $5|p^{2}+1$.
4. The Suzuki group $Sz(2^{p})={}^{2}B_{2}(2^{p})$, where $p$ is an odd prime.
5. The projective special linear group $PSL(3,3)$.

Related facts

• Classification of finite N-groups
• Classification of finite simple groups

References

Journal references

• Nonsolvable finite groups all of whose local subgroups are solvable by John Griggs Thompson, Bulletin of the American Mathematical Society, ISSN 10889485 (electronic), ISSN 02730979 (print), Volume 74, Page 383 - 437(Year 1968): In this paper (appearing across multiple issues of the Pacific Journal of Mathematics), Thompson classified all N-groups.^{WeblinkMore info}