Let n≥5 and 2<t<n.(i) Show that Sn​ cannot act transitively on ... | Filo
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(II) State whether the verb is used transitively or intransitiv... | Filo
(II) State whether the verb is used transitively or intransitiv... | Filo
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Assume G acts transitively on the finite set A and let H be a normal subgroup of G . Let 𝒪1, 𝒪2, …, 𝒪r be the distinct orbits of H on A. (a) Prove that G permutes the sets 𝒪1, 𝒪2, …, 𝒪r in the sense that for each g ∈G and each i ∈{1, …, r} there is a j such that g 𝒪i=𝒪j, where g 𝒪={g ·a |a ∈𝒪} (i.e., in the notation of Exercise 7 the sets 𝒪1, …, 𝒪r are blocks). Prove that G is transitive on {𝒪1, …, 𝒪r} . Deduce that all orbits of H on A have the same cardinality. (b) Prove that if
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