Class-preserving Coleman Automorphisms of Finite Groups with Semidihedral Sylow 2-Subgroups

TL;DR

This paper proves that finite groups with semidihedral Sylow 2-subgroups have class-preserving Coleman automorphisms of odd order, leading to solutions for the normalizer problem and extending previous results in the field.

Contribution

It establishes the odd order of class-preserving Coleman automorphisms for groups with semidihedral Sylow 2-subgroups, advancing understanding of automorphism groups in this context.

Findings

Finite groups with semidihedral Sylow 2-subgroups have class-preserving Coleman automorphisms of odd order.

These groups satisfy the normalizer problem.

The results extend existing literature on automorphisms of such groups.

Abstract

In this paper, we prove that finite groups with semidihedral Sylow 2-subgroup have Class-preserving Coleman outer automorphism group of odd order. As a consequence, these groups satisfy the normalizer problem. In particular, we extend some existing results in the literature concerning class-preserving Coleman automorphisms of finite groups with semidihedral Sylow 2-subgroups.