Results 11 to 20 of about 83,964 (235)

Every group is the outer automorphism group of an HNN-extension of a fixed triangle group [PDF]

Advances in Mathematics, 2017
Fix an equilateral triangle group $T_i=\langle a, b; a^i, b^i, (ab)^i\rangle$ with $i\geq6$ arbitrary. Our main result is: for every presentation $\mathcal{P}$ of every countable group $Q$ there exists an HNN-extension $T_{\mathcal{P}}$ of $T_i$ such ...
Alan D. Logan
semanticscholar   +8 more sources

On conjugacy of maximal abelian subalgebras and the outer automorphism group of the Cuntz algebra [PDF]

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2013
We investigate the structure of the outer automorphism group of the Cuntz algebra and the closely related problem of conjugacy of maximal abelian subalgebras in .
R. Conti, J. Hong, W. Szymański
semanticscholar   +4 more sources

Some finite solvable groups with no outer automorphisms

Journal of Algebra, 1980
A group G is complete if the center Z(G) of G is trivial and if every automorphism of G is inner. In [3], all complete metabelian finite groups were determined. They are either of order 2 or direct products of holomorphs of cyclic groups of different odd prime power orders. Here we will determine all finite groups G which have a normal abelian subgroup
T. M. Gagen
openaire   +4 more sources

Parageometric outer automorphisms of free groups [PDF]

Transactions of the American Mathematical Society, 2007
We study those fully irreducible outer automorphisms ϕ \phi of a finite rank free group F r F_r which are parageometric, meaning that the attracting fixed point of  ϕ \phi in the boundary of outer space is a geometric R \mathbf {R} -tree with respect to ...
Michael Handel, Lee Mosher
  +7 more sources

Outer automorphisms of free Burnside groups [PDF]

Commentarii Mathematici Helvetici, 2013
In this paper, we study some properties of the outer automorphism group of free Burnside groups of large odd exponent. In particular, we prove that it contains free and free abelian subgroups.
Coulon, Rémi
openaire   +6 more sources

Almost-Bieberbach groups with (in)finite outer automorphism group [PDF]

Glasgow Mathematical Journal, 1998
AbstractIf we investigate symmetry of an infra-nilmanifoldM, the outer automorphism group of its fundamental group (an almost-Bieberbach group) is known to be a crucial object. In this paper, we characterise algebraically almost-Bieberbach groupsEwith finite outer automorphism group Out(E).
W. Malfait, A. Szczepański
semanticscholar   +2 more sources

ERRATUM TO FINITELY PRESENTABLE, NON-HOPFIAN GROUPS WITH KAZHDAN'S PROPERTY (T) AND INFINITE OUTER AUTOMORPHISM GROUP [PDF]

, 2005
We give simple examples of Kazhdan groups with infinite outer automorphism groups. This answers a question of Paulin, independently answered by Ollivier and Wise by completely different methods.
Yves Cornulier
semanticscholar   +3 more sources

Outer automorphisms of hypercentral p-groups [PDF]

Glasgow Mathematical Journal, 1995
In his celebrated paper [3] Gaschiitz proved that any finite non-cyclic p-group always admits non-inner automorphisms of order a power of p. In particular this implies that, if G is a finite nilpotent group of order bigger than 2, then Out (G) = Aut(G)/Inn(G) =≠1.
Orazio Puglisi
openaire   +4 more sources

The Structure of the (Outer) Automorphism Group of a Bieberbach Group

Compositio Mathematica, 2003
For any representation \(T\colon F\to\text{Gl}(n,\mathbb{Z})\) of a finite group \(F\), the normalizer \(N_{\text{Gl}(n,\mathbb{Z})}T(F)\) is finitely generated and then, by a theorem of \textit{J. Tits} [J. Algebra 20, 250-270 (1972; Zbl 0236.20032)] this normalizer is either virtually solvable or has a non-Abelian free subgroup. Working with integral
W. Malfait, A. Szczepański
semanticscholar   +3 more sources

A note on separability in outer automorphism groups

Proceedings of the Edinburgh Mathematical Society
AbstractWe give a criterion for separability of subgroups of certain outer automorphism groups. This answers questions of Hagen and Sisto, by strengthening and generalizing a result of theirs on mapping class groups.
Francesco Fournier-Facio
openaire   +4 more sources