On finite groups with nilpotent Sylow-normalizers
It is well known that every finite solvable group possesses a unique conjugacy class of nilpotent self-normalizing subgroups, the so-called Carter subgroups, but it is an open question whether every finite group possesses at most one conjugacy class of Carter subgroups. In this paper, the authors consider the following problem, as a special case of the question above: Is it true that in every finite group G the set \(n(G)=\{N_ G(P)|\) P a Sylow p-subgroup of G for some prime p such that \(N_ G(P)\) is nilpotent\(\}\) is a (possibly empty) set of conjugate subgroups of G? They prove that the answer to this problem is ''yes'' provided the statement is true for all groups G of the form Inn(E)\(\leq G\leq Aut(E)\) where E is a non-abelian finite simple group.
scientific article; zbMATH DE number 3977241