$\kappa$-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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