Results 101 to 110 of about 251 (146)

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
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Normal Automorphisms of Free Groups of Infinitely Based Varieties

Mathematical Notes, 2020
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Adian, S. I., Atabekyan, V. S.
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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
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On automorphisms fixing infinite subgroups of groups

Archiv der Mathematik, 1990
An automorphism of a group G is said to be a power automorphism if it maps every subgroup of G onto itself. The set PAut G of all power automorphisms of G is an abelian normal subgroup of the full automorphism group Aut G, whose properties were investigated by \textit{C. Cooper} [Math. Z. 107, 335-356 (1968; Zbl 0169.338)].
CURZIO, MARIO, FRANCIOSI, SILVANA BARBARA, DE GIOVANNI, FRANCESCO, F.   +3 more
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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.
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Quasi-power automorphisms of infinite groups

Communications in Algebra, 1993
A power automorphism of a group G is an automorphism fixing every subgroup of G. Power automorphisms have been studied by many authors, mainly by C.D.H. Cooper [2]. The set PAutG of all power automorphisms of a group G is a normal, abelian, residually finite subgroup of the full automorphism group AutG of G.
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Infinite generation of automorphism groups of free pro-p groups

Siberian Mathematical Journal, 1993
The author considers the automorphism group of a free pro-\(p\) group as well as the automorphism group of a free profinite group \(F_ n\). The results concern uniformly saturated pro-\(p\) groups. It is proved that if \(G_ 0\) is a saturated pro-\(p\) group, then the completed group algebra \(\widehat {S} =Z/_ p Z[[G_ 0]]\) satisfies the maximal ...
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An infinite family of braid group representations in automorphism groups of free groups

Journal of Knot Theory and Its Ramifications, 2020
The [Formula: see text]-fold ([Formula: see text]) branched coverings on a disk give an infinite family of nongeometric embeddings of braid groups into mapping class groups. We, in this paper, give new explicit expressions of these braid group representations into automorphism groups of free groups in terms of the actions on the generators of free ...
Chang, Wonjun, Kim, Byung Chun, Song, Yongjin   +2 more
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GROUPS OF AUTOMORPHISMS OF INFINITE-DIMENSIONAL SIMPLE LIE ALGEBRAS

Mathematics of the USSR-Izvestiya, 1969
We explicitly describe the groups of automorphisms of the four canonical series of infinite-dimensional simple topological Lie algebras.
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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 ...
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