Abstract. A quantum computer can efficiently find the order of an element in a group, factors of composite integers, discrete logarithms, stabilisers in Abelian groups, and hidden ...
Abstract. The group isomorphism problem asks whether two given groups are isomorphic or not. Whereas the case where both groups are abelian is well understood and can be solved eff...
We investigate the provability of some properties of abelian groups and quadratic residues in variants of bounded arithmetic. Specifically, we show that the structure theorem for...
It is well known that every finite abelian group G can be represented as a direct product of cyclic groups: G ∼= G1 × G2 × · · · × Gt, where each Gi is a cyclic group of ...
We give necessary and sufficient conditions for the first-order theory of a finitely presented abelian lattice-ordered group to be decidable. We also show that if the number of gen...