

A247692


Minimal absolute discriminants a(n) of complex quadratic fields with 3class group of type (3,3), 3principalization type E.6 (1122), and second 3class group G of odd nilpotency class cl(G)=2(n+2)+1.


6




OFFSET

0,1


COMMENTS

The 3principalization type (transfer kernel type, TKT) E.6 (1122) is not a permutation and has a single fixed point.
The nilpotency condition cl(G)=2n+5 for the second 3class group is equivalent to a transfer target type, TTT (called IPAD by Boston, Bush and Hajir) of the shape [(3^{n+2},3^{n+3}),(3,3,3),(3,9)^2].
The second 3class group G is a vertex of depth 1 on the coclass tree with root SmallGroup(243,6) contained in the coclass graph G(3,2).
All these fields possess a Hilbert 3class field tower of exact length 3.
A247692 is an extremely sparse subsequence of A242878 and it is exceedingly hard to compute a(n) for n>0.


LINKS



EXAMPLE

For a(0)=15544, we have the ground state of TKT E.6 with TTT [(9,27),(3,3,3),(3,9)^2] and cl(G)=5.
For a(1)=268040, we have the first excited state of TKT E.6 with TTT [(27,81),(3,3,3),(3,9)^2] and cl(G)=7.
a(0) and a(1) are due to D. C. Mayer (2012).
a(2) and a(3) are due to N. Boston, M. R. Bush and F. Hajir (2013).


CROSSREFS



KEYWORD

hard,more,nonn


AUTHOR



STATUS

approved



