Results 111 to 120 of about 259 (146)

On central automorphisms of infinite groups

Communications in Algebra, 1994
Silvana Franciosi, Francesco De Giovanni, Martin L Newell   +2 more
exaly   +3 more sources

Infinite locally dihedral groups as automorphism groups

Ricerche di Matematica, 2014
It is well-known that there exist groups which cannot be realized as full automorphism group of any group, obvious examples being the (non-trivial) cyclic groups of odd order and (non-trivial) free groups. It was proved by \textit{D. J. S. Robinson} [Q. J. Math., Oxf. II. Ser.
CELENTANI, MARIA ROSARIA, LEONE, ANTONELLA, NICOTERA, Chiara   +2 more
openaire   +2 more sources

Automorphism Groups of Infinite Semilinear Orders (I)

Proceedings of the London Mathematical Society, 1989
Results are obtained concerning the automorphism groups of certain infinite semilinear orders. In particular, countable 2-homogeneous semilinear orders and certain generalizations are examined. It is shown that the automorphism group of such a structure has a unique largest proper normal subgroup, a unique smallest non-trivial normal subgroup, and \(2^{
Droste, M., Holland, W. C., Macpherson, H. D.   +2 more
openaire   +1 more source

Infinite generation of automorphism groups

1989
Let G(n) be the free group of finite rank n in a variety V. Since 1982, it has been known that Aut G(n), the automorphism group of G(n), may not be finitely generated for certain n. But is it always true that Aut G(n) is finitely generated for all but a few number of dimensions n?
Seymour Bachmuth, H. Y. Mochizuki
openaire   +1 more source

Normal Automorphisms of Free Groups of Infinitely Based Varieties

Mathematical Notes, 2020
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Adian, S. I., Atabekyan, V. S.
openaire   +1 more source

Finite Groups Which are Automorphism Groups of Infinite Groups Only

Canadian Mathematical Bulletin, 1985
AbstractThe object of this paper is to exhibit an infinite set of finite semisimple groups H, each of which is the automorphism group of some infinite group, but of no finite group. We begin the construction by choosing a finite simple group S whose outer automorphism group and Schur multiplier possess certain specified properties.
openaire   +2 more sources

The infinite dihedral group as automorphism group.

2002
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F. DE GIOVANNI, RUSSO, Alessio
openaire   +3 more sources

On the Automorphisms of Infinite Chevalley Groups

Canadian Journal of Mathematics, 1969
In (8, § 3.2) Steinberg proved the following result.THEOREM. Let K be a finite field, G′ a simple Chevalley group (“normal type1”) over K. Then every automorphism of G’ is the composite of inner, graph, field, and diagonal automorphisms.For the meaning of these notions, see (8).
openaire   +1 more source

The Construction of Fields with Infinite Cyclic Automorphism Group

Canadian Journal of Mathematics, 1965
This paper deals with a problem raised in a paper by J. de Groot (1): Do there exist fields Ω whose full automorphism group is isomorphic to the additive group of integers Z?The answer to this question is yes. In this paper we construct, given any subfield k of the complex numbers, extension fields Ω of k such that the automorphism group G(Ω/k) of Ω ...
openaire   +1 more source

Algebraic curves with an infinite automorphism group

Mathematical Notes of the Academy of Sciences of the USSR, 1978
Irreducible algebraic curves X (not necessarily smooth and complete) for which the group Aut X of biregular automorphisms is infinite are classified. Applications of the results obtained to the theory of algebraic transformation groups are given.
openaire   +2 more sources