This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A359291 #23 Feb 10 2023 21:13:30 %S A359291 89751,235796,1006931,1996091,2187064 %N A359291 Absolute discriminants of imaginary quadratic fields with elementary bicyclic 5-class group and capitulation type the identity permutation. %C A359291 An algebraic number field with this capitulation type has a 5-class field tower of precise length 2 with Galois group isomorphic to the Schur sigma-group SmallGroup(3125,14). It is a solution to the problem posed by Olga Taussky-Todd in 1970. %D A359291 A. Azizi et al., 5-Class towers of cyclic quartic fields arising from quintic reflection, Ann. math. Québec 44 (2020), 299-328. (p. 314) %D A359291 D. C. Mayer, The distribution of second p-class groups on coclass graphs, J. Théor. Nombres Bordeaux 25 (2013), no. 2, 401-456. (Sec. 3.5.2, p. 448) %H A359291 A. Azizi et al., <a href="https://arxiv.org/abs/1909.03407">5-Class towers of cyclic quartic fields arising from quintic reflection</a>, arXiv:1909.03407 [math.NT], 2019. %H A359291 T. Bembom, <a href="https://ediss.uni-goettingen.de/handle/11858/00-1735-0000-000D-F05F-8">The capitulation problem in class field theory</a>, Dissertation, Univ. Göttingen, 2012. (Sec. 6.3, p. 128) %H A359291 D. C. Mayer, <a href="http://arxiv.org/abs/1403.3833">The distribution of second p-class groups on coclass graphs</a>, arXiv:1403.3833 [math.NT], 2014. %H A359291 O. Taussky-Todd, <a href="https://eudml.org/doc/150989">A remark concerning Hilbert's Theorem 94</a>, J. reine angew. Math. 239/240 (1970), 435-438. %e A359291 The first imaginary quadratic field with 5-class group (5,5) and identity capitulation (123456) has discriminant -89751 and was discovered by Daniel C. Mayer on 03 November 2011. It has ordinal number 31 in the sequence A359871 of all imaginary quadratic fields with 5-class group (5,5). The discriminant -89751 appears in the table on page 130 in the Ph.D. thesis of Tobias Bembom, 2012. However, contrary to his assertion in Remark 2 on page 129, his method was not able to detect the identity capitulation. Consequently, Bembom only found a (non-identity) permutation (135246) but did not solve Taussky's problem. %Y A359291 Cf. A359296. %K A359291 nonn,more,hard %O A359291 1,1 %A A359291 _Daniel Constantin Mayer_, Dec 24 2022