We study the question of the surjectivity of the Galois correspondence from subHopf algebras to subfields given by the Fundamental Theorem of Galois Theory for abelian Hopf Galois structures on a Galois extension of fields with Galois group Γ, a finite abelian p-group. Applying the connection between regular subgroups of the holomorph of a finite abelian p-group (G,+) and associative, commutati...

Is every locally compact abelian group which admits a Heisenberg central extension isomorphic to the product of a locally compact abelian group and its Pontryagin dual? An affirmative answer is obtained for all the commonly occurring types of abelian groups having Heisenberg central extensions, including Lie groups and certain finite Cartesian products of local fields and adèles. Furthermore, f...

We study the computational problem of checking whether a logical sentence is true in a finite abelian group. We prove that model checking first-order sentences on finite abelian groups is fixed-parameter tractable, when parameterized by the size of the sentence. We also prove that model checking monadic second-order sentences on finite abelian groups finitely presented by integer matrices is no...

— In this paper, building among others on earlier works by U. Krause and C. Zahlten (dealing with the case of cyclic groups), we obtain a new upper bound for the little cross number valid in the general case of arbitrary finite Abelian groups. Given a finite Abelian group, this upper bound appears to depend only on the rank and on the number of distinct prime divisors of the exponent. The main ...

A definition of atomic codeword for a group code is presented. Some properties of atomic codewords of group codes are investigated. Using these properties, it is shown that every minimal tail-biting trellis for a group code over a finite abelian group can be constructed from its characteristic generators, which extends the work of Koetter and Vardy who treated the case of a linear code over a f...

A group homomorphism η : A → H is called a localization of A if every homomorphism φ : A→ H can be ‘extended uniquely’ to a homomorphism Φ : H → H in the sense that Φη = φ. This categorical concept, obviously not depending on the notion of groups, extends classical localizations as known for rings and modules. Moreover this setting has interesting applications in homotopy theory, see the introd...

A group homomorphism η : A → H is called a localization of A if every homomorphism φ : A → H can be ‘extended uniquely’ to a homomorphism Φ : H → H in the sense that Φη = φ. This categorical concepts, obviously not depending on the notion of groups, extends classical localizations as known for rings and modules. Moreover this setting has interesting applications in homotopy theory, see the intr...

We exhibit a subset of a finite Abelian group, which tiles the group by translation, and such that its tiling complements do not have a common spectrum (orthogonal basis for their L space consisting of group characters). This disproves the Universal Spectrum Conjecture of Lagarias and Wang [7]. Further, we construct a set in some finite Abelian group, which tiles the group but has no spectrum. ...

Let G be a non-abelian finite group. In this paper, we prove that Γ(G) is K4-free, if and only if G ∼= A× P , where A is an abelian group, P is a 2-group and G/Z(G) ∼= Z2 × Z2. Also, we show that Γ(G) is K1,3-free if and only if G ∼= S3, D8 or Q8.

A group in which every element commutes with its endomorphic images is called an E-group. If p is a prime number, a p-group G which is an E-group is called a pE-group. Every abelian group is obviously an E-group. We prove that every 2-generator E-group is abelian and that all 3-generator E-groups are nilpotent of class at most 2. It is also proved that every infinite 3-generator E-group is abel...