119 research outputs found
Automorphisms of Higher Rank Lamplighter Groups
Let denote the group whose Cayley graph with respect to a
particular generating set is the Diestel-Leader graph , as described
by Bartholdi, Neuhauser and Woess. We compute both and
for , and apply our results to count twisted
conjugacy classes in these groups when . Specifically, we show that
when , the groups have property , that is,
every automorphism has an infinite number of twisted conjugacy classes. In
contrast, when the lamplighter groups have property if and only if .Comment: 28 page
Groups generated by 3-state automata over a 2-letter alphabet, I
An approach to a classification of groups generated by 3-state automata over
a 2-letter alphabet and the current progress in this direction are presented.
Several results related to the whole class are formulated. In particular, all
finite, abelian, and free groups are classified. In addition, we provide
detailed information and complete proofs for several groups from the class,
with the intention of showing the main methods and techniques used in the
classification.Comment: 37 pages, 52 figure
The lamplighter group of rank two generated by a bireversible automaton
We construct a 4-state 2-letter bireversible automaton generating the
lamplighter group of rank two. The action of the
generators on the boundary of the tree can be induced by the affine
transformations on the ring of formal power series over
.Comment: 18 pages, 2 figure
- β¦