School of Mathematical Sciences

Random constructions of countable abelian p-groups menu

Random constructions of countable abelian p-groups

Manfred Droste (Leipzig)
Fri, 16/04/2010 - 17:30
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 Gf, having the set of natural numbers as its domain, with Ulm invariants ≤ f. We then show that with probability 1, Gf has precisely 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).