Speaker:

Manfred Droste (Leipzig)

Date/Time:

Fri, 16/04/2010 - 17:30

Room:

M103

Seminar series:

Joint Combinatorics Study Group/Pure Mathematics Seminar

By Ulm's theorem, countable reduced abelian *p*-groups are characterized, uniquely up to isomorphism, by their Ulm invariants. Given a sequence *f* of Ulm invariants, we provide a probabilistic construction of a countable abelian *p*-group *G _{f}*, having the set of natural numbers as its domain, with Ulm invariants ≤

*f*. We then show that with probability 1,

*G*has precisely

_{f}*f*as its sequence of Ulm invariants. This establishes the existence part of Ulm's theorem in a probabilistic way. We also develop new results for valuated abelian

*p*-groups which are essential for our construction.

Joint work with Ruediger Goebel (Essen).