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Stable rational cohomology of automorphism groups of free groups and the integral cohomology of moduli spaces of graphs.

Craig A. Jensen (2002)

Publicacions Matemàtiques

It is not known whether or not the stable rational cohomology groups H*(Aut(F∞);Q) always vanish (see Hatcher in [5] and Hatcher and Vogtmann in [7] where they pose the question and show that it does vanish in the first 6 dimensions). We show that either the rational cohomology does not vanish in certain dimensions, or the integral cohomology of a moduli space of pointed graphs does not stabilize in certain other dimensions. Similar results are stated for groups of outer automorphisms. This yields...

Strong boundedness and algebraically closed groups

Barbara Majcher-Iwanow (2007)

Commentationes Mathematicae Universitatis Carolinae

Let G be a non-trivial algebraically closed group and X be a subset of G generating G in infinitely many steps. We give a construction of a binary tree associated with ( G , X ) . Using this we show that if G is ω 1 -existentially closed then it is strongly bounded.

Structure of unitary groups over finite group rings and its application

Jizhu Nan, Yufang Qin (2010)

Czechoslovak Mathematical Journal

In this paper, we determine all the normal forms of Hermitian matrices over finite group rings R = F q 2 G , where q = p α , G is a commutative p -group with order p β . Furthermore, using the normal forms of Hermitian matrices, we study the structure of unitary group over R through investigating its BN-pair and order. As an application, we construct a Cartesian authentication code and compute its size parameters.

Su certe classi di gruppi unipotenti

G. Falcone (2005)

Bollettino dell'Unione Matematica Italiana

Si presentano alcuni risultati che caratterizzano i gruppi algebrici unipotenti aventi come reticolo dei sottogruppi connessi una catena e si discutono alcuni risultati conseguenti.

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