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Invariant Sylow subgroups and solvability of finite groups
Let A and G be finite groups of relatively prime orders and assume that A acts on G via automorphisms. We study how certain conditions on G imply its...
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On finite groups with automorphisms whose fixed points are Engel
The main result of the paper is the following theorem. Let q be a prime, n a positive integer, and A an elementary abelian group of order q ...
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Finite groups with a given absolute central factor group
Let G be a group and L ( G ) be the absolute center of G , that is, the set of all elements of G fixed by all automorphisms of G . In this paper, we...
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The Bogomolov multiplier of rigid finite groups
The Bogomolov multiplier of a finite group G is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after...
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Centralizers of coprime automorphisms of finite groups
Let A be an elementary abelian group of order p k with k ≥ 3 acting on a finite p ′-group G . The following results are proved. If γ k -2 ( C ...
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An algorithm to identify automorphisms which arise from self-induced interval exchange transformations
We give an algorithm to determine if the dynamical system generated by a positive automorphism of the free group can also be generated by a...
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Nilpotency of finite groups with Frobenius groups of automorphisms
Suppose that a finite group G admits a Frobenius group of automorphisms BC of coprime order with kernel B and complement C such that C ...
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On a conjecture about automorphisms of finite p-groups
Let G be a nonabelian finite p -group. A longstanding conjecture asserts that G admits a noninner automorphism of order p . In this paper, we prove...
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Large orbits of elements centralized by a Sylow subgroup
If G has a nilpotent normal p -complement and V is a finite, faithful and completely reducible G -module of characteristic p , we prove that there exist
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The automorphism group of a split metacyclic 2-group and some groups of crossed homomorphisms
In this paper we find the structure for the automorphism group of a split metacyclic 2-group G . It can be seen as a continuation of the paper (Curran...
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A simple example of two p-groups with the same automorphism group
It is an open problem whether there exist two different p -groups with the same automorphism group. In this paper, we give a positive answer to this...
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On orbits of automorphism groups II
Let G be a finite group, let A be a group of automorphisms of G and let C G ( A ) denote the subgroup of fixed points of A in G . If the order of C ...
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Automorphisms of direct products of finite groups II
In this paper we first find the automorphism group of the direct product of n copies of an indecomposable non-abelian group. We describe the...
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The automorphism group of a nonsplit metacyclic p-group
This note considers a finite group G = HK , which is a product of a subgroup H and a normal subgroup K , and determines subgroups of Aut G . The special...
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The automorphism group of a split metacyclic 2-group
This paper finds the order, structure and presentation for the automorphism group of any split metacyclic 2-group.
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The automorphism group of a split metacyclic p-group
This paper finds the order, structure and presentation for the automorphism group of a split metacyclic p -group, where p is odd.