A graph-theoretic description of scale-multiplicative semigroups of automorphisms

Cheryl E. Praeger, Jacqui Ramagge, George A. Willis

Research output: Contribution to journalArticlepeer-review


It is shown that a flat subgroup, H, of the totally disconnected, locally compact group G decomposes into a finite number of subsemigroups on which the scale function is multiplicative. The image, P, of a multiplicative semigroup in the quotient, H/H(1), of H by its uniscalar subgroup has a unique minimal generating set which determines a natural Cayley graph structure on P. For each compact, open subgroup U of G, a graph is defined and it is shown that if P is multiplicative over U then this graph is a regular, rooted, strongly simple P-graph. This extends to higher rank the result of R. Möller that U is tidy for x if and only if a certain graph is a regular, rooted tree.

Original languageEnglish
Pages (from-to)221-265
Number of pages45
JournalIsrael Journal of Mathematics
Issue number1
Publication statusPublished - 1 Mar 2020


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