Certain subgroups of the groups Aut(Fn) of automorphisms of a free group Fn are considered. Comparing Alexander polynomials of two poly-free groups Cb+4 and P4 we prove that these groups are not isomorphic, despite the fact that they have a lot of common properties. This answers the question of Cohen-Pakianathan-Vershinin-Wu from [8]. The questions of linearity of subgroups of Aut(Fn) are consi...

Let $L_{n}$ be the free Lie algebra of rank $n$ over a field $K$ characteristic zero, $L_{n,c}=L_{n}/(L_{n}''+\gamma_{c+1}(L_{n}))$ metabelian nilpotent class $c$ algebra, and $F_{n}=L_{n}/L_{n}''$ generated by $x_1,\ldots,x_n$ zero. We call polynomial $p(X_n)$ in these algebras {\it symmetric} if $p(x_1,\ldots,x_n)=p(x_{\pi(1)},\ldots,x_{\pi(n)})$ for each element symmetric group $S_n$. The se...

Abst ract . A c -a utomaton is a part icularl y sim ple type of cellu la r automaton on a grap h; each cell is either in stale 0 or 1 and the next sta te of a cell is determined by addi ng the sta tes of it s neighbors modulo two . Using algebraic an d gra ph-theoretic techniques, questions such as reversibility and existe nce of predecessor configura tions of th ese automata will be st udied ....

If the relation E is transitive, i.e., if (x, y) E E and (y, z) E E imply that (x, z) E E, we speak of a transitive tournament or a total order. Clearly (Z, <) is a total order. We tend to visualize tournaments by considering every edge (x, y) E E as an arrow leading from x to y. In this sense every tournament can also be considered as a complete graph in which every edge is oriented in some di...

This chapter models quantum and neural uncertainty using a concept of the Agent–based Uncertainty Theory (AUT). The AUT is based on complex fusion of crisp (non-fuzzy) conflicting judgments of agents. It provides a uniform representation and an operational empirical interpretation for several uncertainty theories such as rough set theory, fuzzy sets theory, evidence theory, and probability theo...

A model M of cardinality λ is said to have the small index property if for every G ⊆ Aut(M) such that [Aut(M) : G] ≤ λ there is an A ⊆ M with ∣

Let X be a 2-dimensional right-angled hyperbolic building. We characterise the set of covolumes of uniform lattices in Aut(X). We also show that the group Aut(X) admits an infinite ascending tower of uniform lattices.

Baumslag conjectured in the 1970s that the automorphism tower of a finitely generated free group (free nilpotent group) must be very short. Dyer and Formanek [9] justified the conjecture concerning finitely generated free groups in the “sharpest sense” by proving that the automorphism group Aut(Fn) of a non-abelian free group Fn of finite rank n is complete. Recall that a group G is said to be ...

We give matrix and supergravity descriptions of type IIA F-strings polarizing into cylindrical D2 branes. When a RR four-form field strength F4 is turned on in a supersymmetric fashion (with 4 supercharges) , a complete analysis of the solutions reveals the existence of a moduli space of F1 → D2 polarizations (Caesar) for some fractional strengths of the perturbation, and of no polarization wha...