Compact groups having almost discrete orbit hypergroups |
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Authors: | Michael Voit |
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Institution: | (1) Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany |
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Abstract: | LetG be a compact group of automorphism acting continuously on a compact groupH. Then the orbit spaceH
G is a compact hypergroup. We characterize, all solvable groupsH and compact automorphism groupsG for whichH
G is almost discrete, i.e.,H
G is homeomorphic to the one-point-compactification of . It turns out that thenH is isomorphic either to the infinite direct product (p) of the cyclic groups (p) or to
p
n
(
p
the group of allp-adic numbers) for some primep and some . The almost discrete orbit hypergroupsH
G are determined explicitly for some examples. |
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Keywords: | 20E18 43A62 20N20 |
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