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The paper demonstrates relationships between compact Lie groups and orthogonal subgroups, indicating new insights for higher dimensions.
Let G be a compact Lie group of homeomorphisms of R m .The Naive conjecture saying that G is conjugate to a subgroup of the orthogonal group O(m) is known to be false for higher dimension.In this paper we give a partial answer by considering the action of the groupfor 1 i q , and we show that G is contained in S if and only if every element of G centralizes S .
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K. Ben Rejeb (2021) studied this question.
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