New characteristic subgroups for p-stable finite groups and fusion systems ☆

For a p-group S, we define a new characteristic subgroup Q(e)(S) of S. We prove that Q(e)(S) is also a characteristic subgroup for p-stable finite groups of characteristic p having S as a Sylow subgroup. The present paper also establishes that Q(e)(S) is a normal subgroup of any p-stable fusion system over S. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar