$\kappa$-fold transitive groups

by Herden and Shelah. [HeSh:929]
Forum Math, 2010
A group G of type 0 is called kappa-transitive for some cardinal kappa >0 if for any ordered pair of pure elements x,y in G there exist exactly kappa-many phi in Aut G such that xphi =y . We shows the existence of large kappa-transitive groups for every kappa >= aleph_0 assuming V=L and ZFC respectively.

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