Ulm Theorem

One more name from the name index mention in the previous posts was "Ulm". The text spoke about "Ulm theorem", "Ulm sequence". Again, with no initial. Internet search gives "Ulm" most often related to "Ulm University", and "theorem" is so common word. Nevertheless, rather quickly I found:

H. Ulm proved in 1933 that the structure of a reduced countable Abelian p-group is completely determined up to isomorphism by a sequence of invariants called the Ulm invariants. The original methods he invented for the computation of these invariants and the construction of isomorphisms require a transfinite iteration whose length, depending on the group, can be any arbitrarily large countable ordinal. One may therefore ask whether there is an alternative algorithm that requires only transfinite recursions with bounded countable lengths.

[Carry Lee, Borel Isomorphism Relations of Countable Reduced Abelian p-Groups, Oct 14, 1997]

Further search led to the review of the original article [Ulm, H. Zur Theorie der abzählbar-unendlichen Abelschen Gruppen. (German) Math. Ann. 107, 774-803 (1933) and others] in Zentralblatt.

The most interesting finding was the book:
Franz Lemmermeyer und Peter Roquette, Helmut Hasse und Emmy Noether, Die Korrespondenz 1925-1935, Universitätsverlag Göttingen, 2006.

In the section "Kurzbiographien" we read:

Ulm, Helmut (21.06.1908 Gelsenkirchen – )
Studierte 1926–1930 in G¨ottingen, Jena und Bonn; dort promovierte er 1930, und wurde 1947 als Professor an die Universit¨at M¨unster berufen.

[about him]
R. G¨obel, Helmut Ulm: His work and its impact on recent mathematics, Contemporary mathematics AMS 87 (1989), 1-10.


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