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Mathematics, 30.07.2019 23:30 aubreyfoster

Let g be a group of order 9, and let x be a set of cardinality 8. suppose g admits a left group action on x. prove that this group must have a fixed point; that is, prove that there exists x ∈ x such that for all g ∈ g, we have g · x = x. equivalently, prove that there exists x ∈ x such that ox = {x}.

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