We reconsider the role of Lorentz invariance in the dynamical generation of the observed internal symmetries. We argue that, generally, Lorentz invariance can be imposed only in the sense that all Lorentz noninvariant effects caused by the spontaneous breakdown of Lorentz symmetry are physically unobservable. The application of this principle to the most general relativistically invariant Lagra...

A group G is said to be n-centralizer if its number of element centralizers $$\mid {{\,\mathrm{Cent}\,}}(G)\mid =n$$ , an F-group every non-central centralizer contains no other and a CA-group all are abelian. For any non-abelian G, we prove that \frac{G}{Z(G)}\mid \le (n-2)^2$$ $$n 12$$ 2(n-4)^{{log}_2^{(n-4)}}$$ otherwise, which improves earlier result. We arbitrary F-group, then gcd $$(n-2, ...

We extend the notion of a purely infinite simple C*-algebra to the context of unital rings, and we study its basic properties, specially those related to K-Theory. For instance, if R is a purely infinite simple ring, then K0(R) + = K0(R), the monoid of isomorphism classes of finitely generated projective R-modules is isomorphic to the monoid obtained from K0(R) by adjoining a new zero element, ...

For non-negative integers $k\leq n$, we prove a combinatorial identity for the $p$-binomial coefficient $\binom{n}{k}_p$ based on abelian p-groups. A purely proof of this is not known. While proving identity, $r\in \mathbb{N}\cup\{0\},s\in \mathbb{N}$ and $p$ prime, present formula number subgroups $\mathbb{Z}^s$ finite index $p^r$ with quotient isomorphic to $p$-group type $\underline{\lambda}...

A set of quasi-uniform random variables X1, . . . , Xn may be generated from a finite group G and n of its subgroups, with the corresponding entropic vector depending on the subgroup structure of G. It is known that the set of entropic vectors obtained by considering arbitrary finite groups is much richer than the one provided just by abelian groups. In this paper, we start to investigate in mo...

We prove that the near hexagon Q(5,2)× L3 has a non-abelian representation in the extra-special 2-group 21+12 + and that the near hexagon Q(5,2)⊗Q(5,2) has a non-abelian representation in the extra-special 2-group 21+18 − . The description of the non-abelian representation of Q(5,2)⊗Q(5,2) makes use of a new combinatorial construction of this near hexagon.

We study the computational complexity of the isomorphism and equivalence problems on systems of equations over a fixed finite group. We show that the equivalence problem is in P if the group is Abelian, and coNP-complete if the group is non-Abelian. We prove that if the group is non-Abelian, then the problem of deciding whether two systems of equations over the group are isomorphic is coNP-hard...

let $a$ be an abelian topological group and $b$ a trivial topological $a$-module. in this paper we define the second bilinear cohomology with a trivial coefficient. we show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...