Finite groups with some solvable SNS-groups (Q6635340)

A finite group is called an SNS-group if every subgroup is either subnormal or self-normalizing. Clearly, a simple SNS-group has every subgroup self-centralizing.The authors prove many interesting results related to this definition, one of which is the following:\N\NTheorem 3.5. Let \(G\) be a finite non-abelian simple group all of whose maximal subgroups are SNS groups. Then \(G\) is isomorphic to \(\mathrm{PSL}_{2}(2^{p})\) for some prime \(p\) where \(2^{p}-1\) is also prime.