Finitary linear images of finitary linear groups.
Finite Groups of Exponent 4 as Automorphism Groups. II.
Finite-finitary, polycyclic-finitary and Chernikov-finitary automorphism groups
If X is a property or a class of groups, an automorphism ϕ of a group G is X-finitary if there is a normal subgroup N of G centralized by ϕ such that G/N is an X-group. Groups of such automorphisms for G a module over some ring have been very extensively studied over many years. However, for groups in general almost nothing seems to have been done. In 2009 V. V. Belyaev and D. A. Shved considered the general case for X the class of finite groups. Here we look further at the finite case but our main...
Finitely Generated pro-2 Groups with a free subgroup of Index 2.
First-order definability and algebraicity of the sets of annihilating and generating collections of elements for some relatively free solvable groups.
Fixed points of endomorphisms of certain free products
The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.
Fixed points of endomorphisms of certain free products
The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.
Fractal representation of the attractive lamination of an automorphism of the free group
In this paper, we extend to automorphisms of free groups some results and constructions that classically hold for morphisms of the free monoid, i.e., the so-called substitutions. A geometric representation of the attractive lamination of a class of automorphisms of the free group (irreducible with irreducible powers (iwip) automorphisms) is given in the case where the dilation coefficient of the automorphism is a unit Pisot number. The shift map associated with the attractive symbolic lamination...