| Abstrakt: |
A subset X of a group G is called P-small (almost P-small) if there exists an injective sequence (gn)n∊w in G such that the subsets (gnX)n∊w are pairwise disjoint (gnX ∩gmX is finite for all distinct n, m), and weakly P-small if, for every n ∊ w, there exist g0,..., gn ∊ G such that the subsets g0X,...,gnX are pairwise disjoint. We generalize these notions and say that X is near P-small if, for every n ∊ w, there exist g0,...,gn ∊ G such that giX∩gjX is finite for all distinct i, j ∊ {0,..., n}. We study the relationships between near P-small subsets and known types of subsets of a group, and the behavior of near P-small subsets under the action of the combinatorial derivation and its inverse mapping. [ABSTRACT FROM AUTHOR] |
