Results 191 to 200 of about 166,013,378 (225)

On the Group of Automorphisms of a Group

The American Mathematical Monthly, 2011
AbstractThis note gives a generalization of the classical result asserting that if the center of a group G is trivial, then so is the center of its automorphism group Aut(G).
Marian Deaconescu, Gary L. Walls
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The Automorphism Groups of the Braid Groups

American Journal of Mathematics, 1981
In the first of two papers published in the Annals in 1947 [3] Emil Artin mentioned the problem of determining all automorphisms of the braid groups (of the Euclidean plane), and in the second [4] took a first step towards a solution. The main result of this paper is a complete determination of these automorphism groups: the outer automorphism group is
Dyer, Joan L., Grossman, Edna K.
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ON THE CENTRE OF THE AUTOMORPHISM GROUP OF A GROUP

Bulletin of the Australian Mathematical Society, 2015
If the centre of a group $G$ is trivial, then so is the centre of its automorphism group. We study the structure of the centre of the automorphism group of a group $G$ when the centre of $G$ is a cyclic group. In particular, it is shown that the exponent of $Z(\text{Aut}(G))$ is less than or equal to the exponent of $Z(G)$ in this case.
Farrokhi D. G., M., Moghaddam, Mohammad Reza R.   +1 more
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Automorphism Groups of Nilpotent Groups

Bulletin of the London Mathematical Society, 1989
Let \({\mathfrak X}\) denote the class of all finitely generated torsion-free nilpotent groups G such that the derived factor group G/G' is torsion- free. For G in \({\mathfrak X}\), let Aut *(G) denote the group of automorphisms of G/G' induced by the automorphism group of G. If G/G' has rank n and we choose a \({\mathbb{Z}}\)-basis for G/G' then Aut *
Bryant, R. M., Papistas, A.
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Automorphisms of the Gersten Group

Siberian Mathematical Journal, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dudkin, F. A., Shaporina, E. A.
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The Automorphism Group of a Lie Group

Transactions of the American Mathematical Society, 1952
Introduction. The group A (G) of all continuous and open automorphisms of a locally compact topological group G may be regarded as a topological group, the topology being defined in the usual fashion from the compact and the open subsets of G (see ?1). In general, this topological structure of A (G) is somewhat pathological.
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Groups of Automorphisms of Tournaments

Order, 2001
The main topic of the paper is to describe the class of weakly associative lattice groups (wal-groups) isomorphic to wal-groups of automorphisms of tournaments. The author shows that the class of wal-groups that can be interpreted as subalgebras of the class of all wal-groups of automorphisms of tournaments is a proper subclass of the class of all wal ...
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Hyperimaginaries and automorphism groups

Journal of Symbolic Logic, 2001
A hyperimaginary is an equivalence class of a type-definable equivalence relation on tuples of possibly infinite length. The notion was recently introduced in [1], mainly with reference to simple theories. It was pointed out there how hyperimaginaries still remain in a sense within the domain of first order logic.
Daniel Lascar, Anand Pillay
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Noetherian Automorphisms of Groups

Mediterranean Journal of Mathematics, 2005
An automorphism α of a group G is called a noetherian automorphism if for each ascending chain $$ X_1 < X_2 < \ldots < X_n < X_{n + 1} < \ldots $$ of subgroups of G there is a positive integer m such that \(X_n^{\alpha} = X_n \) for all n ≥ m. The structure of the group of all noetherian automorphisms of a group is investigated in this paper.
DE GIOVANNI, FRANCESCO, DE MARI, FAUSTO
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Automorphism groups ofFC-groups

Archiv der Mathematik, 1983
Robinson, D. J. S., Stonehewer, S. E., Wiegold, James   +2 more
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