2023/07/26 by Allombert, Bill, Mayer, Daniel C.
#11R16 #11R29 #11R32 #11R37 #20D15 #20E22 #20F05 #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2307.13898
It is proved that c = 689347 = 31*37*601 is the smallest conductor of a cyclic cubic number field K whose maximal unramified pro-3-extension E = F(3,infinity,K) possesses an automorphism group G = Gal(E/K) of order 6561 with coinciding relation and generator rank d2(G) = d1(G) = 3 and harmonically balanced transfer kernels kappa(G) in S(13).