We study some families of finite groups having inner class-preserving automorphisms. In particular, let G be a finite group and S be a semidihedral Sylow 2-subgroup. Then, in both cases when either Sym(4) is not a homomorphic image of G and Z(S) < Z(G) or G is nilpotent-by-nilpotent, we have that all the Coleman automorphisms of G are inner. As a consequence, these groups satisfy the normalizer problem.
COLEMAN AUTOMORPHISMS OF FINITE GROUPS WITH SEMIDIHEDRAL SYLOW 2-SUBGROUPS
Riccardo Aragona
2024-01-01
Abstract
We study some families of finite groups having inner class-preserving automorphisms. In particular, let G be a finite group and S be a semidihedral Sylow 2-subgroup. Then, in both cases when either Sym(4) is not a homomorphic image of G and Z(S) < Z(G) or G is nilpotent-by-nilpotent, we have that all the Coleman automorphisms of G are inner. As a consequence, these groups satisfy the normalizer problem.File in questo prodotto:
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