2021/01/26 by Corson, Samuel M.
#20A15 #20E15 #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)
paper · doi:10.48550/arxiv.2101.11035
A group G is Jónsson if |H| < |G| whenever H is a proper subgroup of G. Using an embedding theorem of Obraztsov it is shown that there exists a Jónsson group G of infinite cardinality κ if and only if there exists a Jónsson algebra of cardinality κ. Thus the question as to which cardinals admit a Jónsson group is wholly reduced to the well-studied question of which cardinals are not Jónsson. As a consequence there exist Jónsson groups of arbitrarily large cardinality. Another consequence is that the infinitary edge-orbit conjecture of Babai is true.