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Preprint Number 1740
1740. Saharon Shelah and Lajos Soukup On κ-homogeneous, but not κ-transitive permutation groups E-mail: Submission date: 4 March 2020 Abstract: A permutation group G on a set A is κ-homogeneous iff for all
X,Y in [A]^κ with |A ∖ X|=|A ∖ Y|=|A| there is a g in
G with g[X]=Y.
G is κ-transitive iff for any injective function f with
dom(f) ∪ ran(f) in [A]^{≤ κ} and |A ∖ dom(f)|=|A ∖
ran(f)|=|A| there is a g in G with f ⊂ g. Mathematics Subject Classification: 03E35, 20B22 Keywords and phrases: |

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