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The (outer) automorphism group of a group extension

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2002
Let \(G\) be a group, \(K\) a normal subgroup of \(G\) and \(Q\cong G/K\). In other words, \(G\) is an extension of \(K\) by \(Q\). Each automorphism of \(G\) which sends \(K\) into itself induces automorphisms respectively on \(K\) and on \(Q\). This subgroup of \(\Aut(G)\) is denoted by \(\Aut(G,K)\).
W. Malfait
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An Ergodic Action of the Outer Automorphism Group of a Free Group [PDF]

GAFA Geometric And Functional Analysis, 2005
.For n > 2, the action of the outer automorphism group of the rank n free group Fn on Hom(Fn, SU(2))/SU(2) is ergodic with respect to the Lebesgue measure class.
W. Goldman
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Outer automorphism groups of ordered permutation groups [PDF]

Forum Mathematicum, 2002
An infinite linearly ordered set (S,<=) is called doubly homogeneous if its automorphism group A(S) acts 2-transitively on it. We show that any group G arises as outer automorphism group G cong Out(A(S)) of the automorphism group A(S), for some doubly homogeneous chain (S,<=).
Manfred Droste, Saharon Shelah
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Outer Automorphisms of Certain p-Groups [PDF]

Proceedings of the American Mathematical Society, 1966
Introduction. By employing methods of Group Representation Theory, the main theorems in this paper establish the existence of outer automorphisms of certain types of p-groups. There is no doubt that the results obtained in ?3 can also be obtained by familiar group theoretic techniques.
Charles F. Godino
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Finite groups of outer automorphisms of free groups [PDF]

Glasgow Mathematical Journal, 1996
Let Fr denote the free group of rank r and Out Fr: = AutFr/Inn Fr the outer automorphism group of Fr (automorphisms modulo inner automorphisms). In [10] we determined the maximal order 2rr! (for r > 2) for finite subgroups of Out Fr as well as the finite subgroup of that order which, for r > 3, is unique up to conjugation. In the present paper we
Bruno Zimmermann
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The existence of outer automorphisms of some groups [PDF]

Proceedings of the American Mathematical Society, 1956
F. Haimo and E. Schenkman [1] raised the question: Does a nilpotent group G always possess an outer automorphism? The answer is in the affirmative if G is finite and nilpotent of class 2, as is seen from a Schenkman's [I ] stronger result. The object of this note is to show that the answer is also in the affirmative for another family of nilpotent ...
Rimhak Ree
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Irreducible outer automorphisms of a free group [PDF]

Proceedings of the American Mathematical Society, 1991
We give sufficient conditions for all positive powers of an outer automorphism of a finitely generated free group to be irreducible, in the sense of Bestvina and Handel. We prove a conjecture of Stallings (1982), that a PV automorphism in rank ≥ 3 \geq 3 has no nontrivial fixed points.
S. M. Gersten, J. R. Stallings
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Outer automorphisms of supersoluble groups [PDF]

Glasgow Mathematical Journal, 2000
In this paper we study the problem of the existence on non-inner automorphisms for the class of torsion-free supersolvable groups, answering a question raised by Robinson.1991 Mathematics Subject Classification 20F16, 20F28.
F. Menegazzo, PUGLISI, ORAZIO
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Kazhdan groups with infinite outer automorphism group [PDF]

Transactions of the American Mathematical Society, 2004
For each countable group $Q$ we produce a short exact sequence $1\to N \to G \to Q\to 1$ where $G$ is f.g. and has a graphical $\frac16$ presentation and $N$ is f.g. and satisfies property $T$.
Y. Ollivier, D. Wise
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Outer automorphisms of ordered permutation groups [PDF]

Proceedings of the Edinburgh Mathematical Society, 1975
A well-known fact is that every automorphism of the symmetric group on a set must be inner (whether the set is finite or infinite) unless the set has exactly six elements (4, § 13). A long-standing conjecture concerns the analogue of this fact for the group A(S) of all order-preserving permutations of a totally ordered set S.
W. Charles Holland
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