46 research outputs found
Parabolic and Quasiparabolic Subgroups of Free Partially Commutative Groups
Let S be a finite graph and G be the corresponding free partially commutative
group. In this paper we study subgroups generated by vertices of the graph S,
which we call canonical parabolic subgroups. A natural extension of the
definition leads to canonical quasiparabolic subgroups. It is shown that the
centralisers of subsets of G are the conjugates of canonical quasiparabolic
centralisers satisfying certain graph theoretic conditions.Comment: 18 pages, 1 figur
Multiplicative measures on free groups
We introduce a family of atomic measures on free groups generated by
no-return random walks. These measures are shown to be very convenient for
comparing "relative sizes" of subgroups, context-free and regular subsets
(that, subsets generated by finite automata) of free groups. Many asymptotic
characteristics of subsets and subgroups are naturally expressed as analytic
properties of related generating functions. We introduce an hierarchy of
asymptotic behaviour "at infinity" of subsets in the free groups, more
sensitive than the traditionally used asymptotic density, and apply it to
normal subgroups and regular subsets.Comment: LaTeX, requires amssymb.sty; 31 pp Version 3: more detail in Example
2 and Tauberian theorem