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Homogeneous Locally Compact Groups

โœ Scribed by Markus Stroppel

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
189 KB
Volume
199
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

We determine all locally compact abelian groups with the property that the group of all topological automorphisms acts transitively on the set of nontrivial elements. Such groups are called homogeneous. The connected ones are the additive groups of finite-dimensional vector spaces over the real numbers. The ลฝ . compact ones are the not necessarily finite powers of cyclic groups of prime order. Actually, the commutativity hypothesis is needed only in the remaining cases: the disconnected torsion-free homogeneous abelian locally compact groups are the divisible hulls of powers of the group of p-adic integers; and the homoge-ลฝ . neous abelian locally compact torsion groups are the products of compact powers of cyclic groups and discrete elementary abelian groups. A characterization of additive groups of vector spaces of finite dimension over locally compact fields is obtained.

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