Sylow 2-subgroups of simple groups (Q2782386)

At the beginning of this article the authors list six problems connected with Sylow 2-subgroups of finite simple groups. Then in the remainder of this paper the authors deal mainly with the problem of finding characterizations of 2-groups which are Sylow 2-subgroups of simple groups. Without using the classification of finite simple groups they define a family of 2-groups such that every Sylow 2-subgroup of a simple group is a member of this class. This necessary condition however is not sufficient as this condition does not distinguish between Sylow 2-subgroups of simple groups and Sylow 2-subgroups of fusion simple groups. The paper closes with a long appendix where all 2-groups of order \(\leq 2^{46}\) are described which are Sylow 2-subgroups of simple groups.NEWLINENEWLINEFor the entire collection see [Zbl 0980.00029].