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

Title: A graph-theoretic description of scale-multiplicative semigroups of automorphisms
Creator: Praeger, Cheryl E.; Ramagge, Jacqui; Willis, George A.
Relation: ARC.DP150100060 http://purl.org/au-research/grants/arc/DP150100060
Relation: Israel Journal of Mathematics Vol. 237, Issue 1, p. 221-265
Publisher Link: http://dx.doi.org/10.1007/s11856-020-2005-0
Publisher: Magnes Press
Resource Type: journal article
Date: 2020
Description: 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.
Subject: subgroup; subsemigroups; automorphisms; multiplicative
Identifier: http://hdl.handle.net/1959.13/1424946
Identifier: uon:38171
Identifier: ISSN:0021-2172
Language: eng
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