Classification of finite N-groups

Statement

Any finite N-group that is not solvable is an almost simple group. In particular, it contains a simple normal centralizer-free subgroup isomorphic to one of the following:

1. The projective special linear group $PSL(2,q)$ for some prime power $q>3$.
2. The Suzuki group $Sz(2^{2n+1})$, $n\geq 1$.
3. The projective special linear group $PSL(3,3)$.
4. The Mathieu group $M_{11}$.
5. The alternating group of degree seven $A_{7}$.
6. The projective special unitary group $PSU(3,3)$.

Related facts

• Classification of finite minimal simple 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}