Results 191 to 200 of about 9,040,817 (231)

Automorphisms of Automorphism Group of Dihedral Groups

Creative Mathematics and Informatics, 2023
The automorphism group of a Dihedral group of order 2n is isomorphic to the holomorph of a cyclic group of order n. The holomorph of a cyclic group of order n is a complete group when n is odd. Hence automorphism groups of Dihedral groups of order 2n are its own automorphism groups whenever n is odd. In this paper, we prove that the result is also true
Sajikumar, Sadanandan, Vinod, Sivadasan, Biju, Gopinadhan Sathikumari   +2 more
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The automorphism group of a graphon [PDF]

Journal of Algebra, 2015
We study the automorphism group of graphons (graph limits). We prove that after an appropriate "standardization" of the graphon, the automorphism group is compact.
László Lovasz, Balázs Szegedy
exaly   +2 more sources

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.
Bettina Eick
exaly   +2 more sources

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
openaire   +1 more source

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.
openaire   +1 more source

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.
openaire   +1 more source

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
openaire   +2 more sources

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.
openaire   +3 more sources

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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On Automorphism Groups of the Fields of Automorphic Functions

The Annals of Mathematics, 1972
The purpose of this paper is to determine the group of all automorphisms of the field generated by automorphic functions with respect to infinitely many mutually commensurable discrete subgroups of the group of all automorphisms of a bounded symmetric domain. In the case where either the dimension of the domain is one or the quotient spaces are compact,
openaire   +2 more sources