we prove that the class of profinite groups $g$ that have a factorization $g=ab$‎ ‎with $a$ and $b$ abelian closed subgroups‎, ‎is closed under taking inverse limits‎ ‎of surjective inverse systems‎. ‎this is a generalization of a recent result by k. h. hofmann and f. g. russo‎. ‎as an application we reprove their generalization of iwasawa's structure theorem for‎ ‎quasihamiltonian pro-$p$...

A partial difference set having parameters (n2, r(n− 1), n+ r2 − 3r, r2 − r) is called a Latin square type partial difference set, while a partial difference set having parameters (n2, r(n+1),−n+r2+3r, r2+r) is called a negative Latin square type partial difference set. Nearly all known constructions of negative Latin square partial difference sets are in elementary abelian groups. In this pape...

We, for any natural n, construct an אn-free abelian groups which have few homomorphisms to Z. For this we use “אn-free (n+1)-dimensional black boxes”. The method is hopefully relevant to other constructions of אn-free abelian groups. I would like to thank Alice Leonhardt for the beautiful typing. This research was supported by German-Israeli Foundation for Scientific Research and Development Fi...

This paper describes a quantum algorithm for efficiently decomposing finite Abelian groups. Such a decomposition is needed in order to apply the Abelian hidden subgroup algorithm. Such a decomposition (assuming the Generalized Riemann Hypothesis) also leads to an efficient algorithm for computing class numbers (known to be at least as difficult as factoring).

A new criterion is established for an abelian group to be free. The criterion is in terms of an ascending chain of free subgroups and is dependent upon a new class of torsion-free groups. The result leads to the construction, for each positive integer n, of a group G of cardinality K that is not free but is X -free. A conjecture in infinitary logic concern71 n ing free abelian groups is also ve...

We consider Donovan's conjecture in the context of blocks groups G with defect group D and normal subgroups N◁G such that G=CD(D∩N)N, extending similar results for abelian groups. As an application we show holds form Q8×C2n or Q8×Q8 defined over a discrete valuation ring.

We deal with some pcf, (posible cofinality theory) investigations mostly motivated by questions in abelian group theory. We concentrate on applications to test problems but we expect the combinatorics will have reasonably wide applications. We almost always answer the test problem which is proving the existence of ℵω-free abelian groups with trivial dual, i.e., with no non-trivial homomorphisms...

We give examples of abelian variety quotients of the modular jacobian J0(N) with nontrivial visible Shafarevich-Tate groups. In computing these examples we developed formulas for invariants of higher dimensional modular abelian varieties.