Automorphism groups of 2-groups
Copyright policy )Automorphism groups of 2-groups
It is conjectured that \(|G|\mid|\Aut(G)|\) for every nonabelian \(p\)-group \(G\). In this paper the following results are proven. Theorem. For every \(s\in\mathbb{N}\) there exists \(o(r,s)\in\mathbb{N}\) such that \(2^s\mid|G|\mid|\Aut(G)|\) for all \(2\)-groups \(G\) of coclass \(r\) and order at least \(o(r,s)\). -- Corollary. Almost all \(2\)-groups of coclass \(r\) satisfy the divisibility conjecture. Intermediate results leading to the above theorems present independent interest.
finite 2-groups, coclass theory, Algebra and Number Theory, Coclass theory, Finite nilpotent groups, \(p\)-groups, automorphism groups, Automorphism groups, Automorphisms of abstract finite groups, Arithmetic and combinatorial problems involving abstract finite groups, 2-Groups
finite 2-groups, coclass theory, Algebra and Number Theory, Coclass theory, Finite nilpotent groups, \(p\)-groups, automorphism groups, Automorphism groups, Automorphisms of abstract finite groups, Arithmetic and combinatorial problems involving abstract finite groups, 2-Groups
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