Results 111 to 120 of about 39,756 (284)
Automorphism groups of 2-groups
Journal of Algebra, 2006 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.
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A Note on the Automorphism Group of a p-Group [PDF]
Proceedings of the American Mathematical Society, 1968 The relation between the order of a p-group and its automorphism group has been the subject of several papers, see [1], [2], and [4]. The existence of outer-automorphisms of a finite p-group was proved by Gaschiitz [3], but the question of the size of the automorphism group of a p-group still remains.
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Assembling homology classes in automorphism groups of free groups [PDF]
, 2015 The observation that a graph of rank n can be assembled from graphs of smaller rank k with s leaves by pairing the leaves together leads to a process for assembling homology classes for Out(Fn) and Aut(Fn) from classes for groups Γk,s, where the Γk,s ...
James F. Conant +3 more
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Bulletin of the London Mathematical Society, Volume 58, Issue 6, June 2026.Abstract Given r⩾3$r \geqslant 3$, we prove that there exists λ>0$\lambda >0$ depending only on r$r$ so that if G$G$ is a metric graph of rank r$r$ with metric entropy 1, then there exists a proper subgraph H$H$ of G$G$ with metric entropy at least λ$\lambda$. This answers a question of the second two authors together with Rieck. We interpret this as a
Tawfiq Hamed, Tarik Aougab, Matt Clay
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Possible Groups of Automorphisms [PDF]
Proceedings of the National Academy of Sciences, 1943 Not ...
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Automorphism Groups of Abelian p-Groups [PDF]
Proceedings of the American Mathematical Society, 1975 Let r be the automorphism group of a nonelementary reduced abelian p-group, p > 5. It is shown that every noncentral norinal subgroup of r contains a noncentral elementary abelian normal p-subgroup of r of rank at least 2. 1. The result. Throughout the following, G is a reduced p-primary abelian group, p > 5, and F is the group of all automorphisms of ...
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Infinite groups with fixed point properties
, 2007 We construct finitely generated groups with strong fixed point properties. Let Xac be the class of Hausdorff spaces of finite covering dimension which are mod–p acyclic for at least one prime p.
G. Arzhantseva +23 more
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On the tightness of left‐invariant contact structures
Bulletin of the London Mathematical Society, Volume 58, Issue 6, June 2026.Abstract We prove that all left‐invariant contact structures on three‐dimensional Lie groups are tight. The argument is based on Riemannian methods and establishes a unique factorization property for any Lie group admitting a left‐invariant contact structure, other than SU(2)$\mathrm{SU}(2)$. We then make use of such factorization property to construct
Eugenio Bellini
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The divisibility conjecture for automorphism groups of finite p-groups [PDF]
Advances in Group Theory and Applications, 2020 Jill Dietz
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Automorphism groups of tree actions and of graphs of groups
, 1996 Let Γ be a group. The minimal non-abelian Γ-actions on real trees can be parametrized by the projective space of the associated length functions. The outer automorphism group of Γ, Out(Γ) = Aut(Γ)ad(Γ), acts on this space.
H. Bass, Renfang Jiang
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