Let Var be the category of complex algebraic varieties, Top that of nice topological spaces, Dab be the derived category of finite complexes of finitely generated abelian groups. One has tensor functors Var → Top → Dab, the first assigns to a variety its space equipped with the classical topology, the second one is the singular chain complex functor (the tensor structure for the first two categ...

An abelian square is the concatenation of two words that are anagrams of one another. A word of length n can contain at most Θ(n) distinct factors, and there exist words of length n containing Θ(n) distinct abelian-square factors, that is, distinct factors that are abelian squares. This motivates us to study infinite words such that the number of distinct abelian-square factors of length n grow...

Let G be a group. We denote by ν(G) certain extension of the non-abelian tensor square G⊗G G×G. In this paper we prove that derived subgroup ν(G)′ is central product three normal subgroups ν(G), all isomorphic to G⊗G. As consequence, describe structure each term and lower series group ν(G).

The energy-momentum tensor (EMT) of the 't Hooft-Polyakov monopole and Julia-Zee dyon are studied. This contains important information about pressure shear force distributions which define mechanical properties systems. Obtaining violation local stability criterion for magnetic we decompose EMTs into long- short-range parts. decomposition depends on Abelian field strength cannot be uniquely def...

Pairings are particular bilinear maps, and as any bilinear maps they factor through the tensor product as group homomorphisms. Besides, nothing seems to prevent us to construct pairings on other abelian groups than elliptic curves or more general abelian varieties. The point of view adopted in this contribution is based on these two observations. Thus we present an elliptic curve free study of ...

Introduction 1 Acknowledgment 1 Notation 1 1. The tensor product with a motive of weight zero 3 1.1. The tensor product of two motives of weight zero 3 1.2. The tensor product of a torus with a motive of weight 0 3 1.3. The tensor product of an abelian scheme with a motive of weight 0 4 1.4. The tensor product of an extension of an abelian scheme by a torus with a motive of weight 0 4 2. The 1-...

Let $G$ be a finite $p$-group. In this paper we obtain bounds for the exponent of non-abelian tensor square $G \otimes G$ and $\nu(G)$, which is certain extension by \times G$. particular, bound $\exp(\nu(G))$ in terms $\exp(\nu(G/N))$ $\exp(N)$ when admits some specific normal subgroup $N$. We also establish $\exp(G G)$ $\exp(G)$ either nilpotency class or coclass group $G$, improving existing...