6,775 research outputs found
On the Word and Period Growth of some Groups of Tree Automorphisms
We generalize a class of groups defined by Rostislav Grigorchuk to a much
larger class of groups, and provide upper and lower bounds for their word
growth (they are all of intermediate growth) and period growth (under a small
additional condition, they are periodic).Comment: to appear in Comm. Algebr
Some Properties of Distal Actions on Locally Compact Groups
We consider the actions of (semi)groups on a locally compact group by
automorphisms. We show the equivalence of distality and pointwise distality for
the actions of a certain class of groups. We also show that a compactly
generated locally compact group of polynomial growth has a compact normal
subgroup such that is distal and the conjugacy action of on
is ergodic; moreover, if itself is (pointwise) distal then is Lie
projective. We prove a decomposition theorem for contraction groups of an
automorphism under certain conditions. We give a necessary and sufficient
condition for distality of an automorphism in terms of its contraction group.
We compare classes of (pointwise) distal groups and groups whose closed
subgroups are unimodular. In particular, we study relations between distality,
unimodularity and contraction subgroups.Comment: 27 pages, main results are revised and improved, some preliminary
results are removed and some new results are added, some proofs are revised
and some are made shorte
Topological groups and infinite graphs
AbstractWe show how results concerning infinite, locally finite, vertex-symmetric graphs can be related with the structure theory of topological groups, when the latter is applied to automorphism groups of the graphs. In particular, we discuss polynomial growth, bounded automorphisms and infinite expanders. In an appendix, we present three problems on infinite graphs, not necessarily linked with topological considerations
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