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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Splitting in map groups

Authors: Lewis Robertson and Theodore W. Wilcox
Journal: Proc. Amer. Math. Soc. 33 (1972), 613-618
MSC: Primary 22D12
MathSciNet review: 0296210
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Abstract: Every locally compact maximally almost periodic group G has a normal vector subgroup, the centralizer of which is of finite index. This vector subgroup is nontrivial whenever the identity component of G is not compact. Furthermore, if G has relatively compact conjugacy classes, then $ G \cong {R^n} \times L$ where L has a compact open normal subgroup. Several structure theorems are also obtained for cases in which splitting need not occur.

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Keywords: Maximally almost periodic, finite-dimensional unitary representation, MAP-groups, $ {[{\text{FC}}]^ - }$-groups, splitting
Article copyright: © Copyright 1972 American Mathematical Society

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