Group-theoretic origin of certain generating function

Programming Research Group THE GROUP THEORETIC ORIGIN OF NON-LOCALITY FOR QUBITS

We describe a general framework in which we can precisely compare the structures of quantum-like theories which may initially be formulated in quite different mathematical terms. We then use this framework to compare two theories: quantum mechanics restricted to qubit stabiliser states and operations, and a toy theory proposed by Spekkens. We discover that viewed within our framework these theo...

Ergodic-theoretic Properties of Certain Bernoulli Convolutions

In [17] the author and A. Vershik have shown that for β = 1 2 (1 + √ 5) and the alphabet {0, 1} the infinite Bernoulli convolution (= the Erdös measure) has a property similar to the Lebesgue measure. Namely, it is quasi-invariant of type II1 under the β-shift, and the natural extension of the β-shift provided with the measure equivalent to the Erdös measure, is Bernoulli. In this note we exten...

Ring Theoretic Properties of Certain Hecke Algebras

In the work of one of us (A.W.) on the conjecture that all elliptic curves defined over Q are modular, the importance of knowing that certain Hecke algebras are complete intersections was established. The purpose of this article is to provide the missing ingredient in [W2] by establishing that the Hecke algebras considered there are complete intersections. As is recorded in [W2], a method going...

On Marginal Automorphisms of a Group Fixing the Certain Subgroup

Let W be a variety of groups defined by a set W of laws and G be a finite p-group in W. The automorphism α of a group G is said to bea marginal automorphism (with respect to W), if for all x ∈ G, x−1α(x) ∈ W∗(G), where W∗(G) is the marginal subgroup of G. Let M,N be two normalsubgroups of G. By AutM(G), we mean the subgroup of Aut(G) consistingof all automorphisms which centralize G/M. AutN(G) ...

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup