In this paper, we exhibit a strong relation between the sand automata configuration space and the cellular automata configuration space. This relation induces a compact topology for sand automata, and a new context in which sand automata are homeomorphic to cellular automata acting on a specific subshift. We show that the existing topological results for sand automata, including the Hedlund-lik...

On the Automorphism Tower of Free Nilpotent Groups Martin Dimitrov Kassabov 2003 In this thesis I study the automorphism tower of free nilpo-tent groups. Our main tool in studying the automorphism tower is to embed every group as a lattice in some Lie group. Using known rigidity results the automorphism group of the discrete group can be embedded into the automorphism group of the Lie group. Th...

By the Shepherd–Leedham-Green–McKay theorem on finite p-groups of maximal class, if a finite p-group of order pn has nilpotency class n−1, then it has a subgroup of nilpotency class at most 2 with index bounded in terms of p. Counterexamples to a rank analogue of this theorem are constructed, which give a negative solution to Problem 16.103 in Kourovka Notebook. Moreover, it is shown that there...

The results of J. F. Qian et al. [5] on (1 − γ)-constacyclic codes over finite chain rings of nilpotency index 2 are extended to (1 − γe)constacyclic codes over finite chain rings of arbitrary nilpotency index e+1. The Gray map is introduced for this type of rings. We prove that the Gray image of a linear (1− γe)-constacyclic code over a finite chain ring is a distance-invariant quasi-cyclic co...

We consider logical deenability of the group-theoretic notions of simplicity, nilpotency and solvability on the class of nite groups. On one hand, we show that these notions are deenable by sentences of deterministic transitive closure logic DTC. These results are based on known group-theoretic results. On the other hand, we prove that simplicity, nilpotency and the normal closure of a subset o...

We call (i?) 1 the Lie ring associated with R, and denote it by 9Î. The question of how far the properties of SR determine those of R is of considerable interest, and has been studied extensively for the case when R is an algebra, but little is known of the situation in general. In an earlier paper the author investigated the effect of the nilpotency of 9î upon the structure of R if R contains ...