On tidy subgroups of locally compact totally disconnected groups
نویسندگان
چکیده
منابع مشابه
Representations of Locally Compact Totally Disconnected Groups
Let G be a locally compact totally disconnected group. Recall that every neighborhood of 1 in G contains a compact open subgroup. If G is assumed to be compact, then every neighborhood of 1 in G contains a compact open normal subgroup. On the other hand, it follows from properties of Lie groups that the group GL(n,C) has the property that there is some neighborhood of the identity which contain...
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Let G be a totally disconnected, locally compact group and let H be a virtually flat (for example, polycyclic) group of automorphisms of G. We study the structure of, and relationships between, various subgroups of G defined by the dynamics of H. In particular, we consider the following four subgroups: the intersection of all tidy subgroups for H on G (in the case that H is flat); the intersect...
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Let α be an automorphism of the totally disconnected group G. The compact open subgroup, V , of G is tidy for α if [α(V ) : α(V ) ∩ V ] is minimised at V , where V ′ ranges over all compact open subgroups of G. Identifying a subgroup tidy for α is analogous to identifying a basis which puts a linear transformation into Jordan canonical form. This analogy is developed here by showing that commut...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2002
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700020530