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Conservative polynomials and yet another action of Gal ( ℚ ¯ / ℚ ) on plane trees

Fedor Pakovich (2008)

Journal de Théorie des Nombres de Bordeaux

In this paper we study an action D of the absolute Galois group Γ = Gal ( ℚ ¯ / ℚ ) on bicolored plane trees. In distinction with the similar action provided by the Grothendieck theory of “Dessins d’enfants” the action D is induced by the action of Γ on equivalence classes of conservative polynomials which are the simplest examples of postcritically finite rational functions. We establish some basic properties of the action D and compare it with the Grothendieck action.

Construction du cœur compact d’un arbre réel par substitution d’arbre

Yann Jullian (2011)

Annales de l’institut Fourier

Étant donné un automorphisme σ d’un groupe libre et un représentant topologique train-track de son inverse, on peut construire un arbre réel T appelé arbre répulsif de σ . Le groupe libre agit sur T par isométries. La dynamique engendrée par σ peut être représentée par l’action du groupe libre restreinte à un sous-ensemble compact bien choisi du complété métrique de T . Cet article construit ce sous-ensemble sur une classe d’exemples en introduisant des opérations appelées substitutions d’arbre ;...

Co-rank and Betti number of a group

Irina Gelbukh (2015)

Czechoslovak Mathematical Journal

For a finitely generated group, we study the relations between its rank, the maximal rank of its free quotient, called co-rank (inner rank, cut number), and the maximal rank of its free abelian quotient, called the Betti number. We show that any combination of the group's rank, co-rank, and Betti number within obvious constraints is realized for some finitely presented group (for Betti number equal to rank, the group can be chosen torsion-free). In addition, we show that the Betti number is additive...

Counting arithmetic subgroups and subgroup growth of virtually free groups

Amichai Eisenmann (2015)

Journal of the European Mathematical Society

Let K be a p -adic field, and let H = P S L 2 ( K ) endowed with the Haar measure determined by giving a maximal compact subgroup measure 1 . Let A L H ( x ) denote the number of conjugacy classes of arithmetic lattices in H with co-volume bounded by x . We show that under the assumption that K does not contain the element ζ + ζ - 1 , where ζ denotes the p -th root of unity over ℚ p , we have lim x → ∞ log A L H ( x ) x log x = q - 1 where q denotes the order of the residue field of K .

Critical constants for recurrence of random walks on G -spaces

Anna Erschler (2005)

Annales de l’institut Fourier

We introduce the notion of a critical constant c r t for recurrence of random walks on G -spaces. For a subgroup H of a finitely generated group G the critical constant is an asymptotic invariant of the quotient G -space G / H . We show that for any infinite G -space c r t ≥ 1 / 2 . We say that G / H is very small if c r t < 1 . For a normal subgroup H the quotient space G / H is very small if and only if it is finite. However, we give examples of infinite very small G -spaces. We show also that critical constants for recurrence can be used...

Crossed product of cyclic groups

Ana-Loredana Agore, Dragoş Frățilă (2010)

Czechoslovak Mathematical Journal

All crossed products of two cyclic groups are explicitly described using generators and relations. A necessary and sufficient condition for an extension of a group by a group to be a cyclic group is given.

Currently displaying 241 – 260 of 1792