Schur's theorem and its generalisation, Baer's theorem, are distinguished results in group theory, connecting the upper central quotients with lower series. The aim of this paper is to generalise these two different directions, using novel methods related non-abelian tensor product. In particular, we prove a version Schur–Baer for finitely generated groups. Then, apply newly obtained describe k...

In the article, we find new dilatation results on non-commutative $$L^p$$ spaces. We prove that any self-adjoint, unital, positive measurable Schur multiplier some $$B(L^2(\Sigma ))$$ admits, for all $$1\leqslant p<\infty $$ , an invertible isometric dilation -space. obtain a similar result completely Fourier VN(G), when G is unimodular locally compact group. Furthermore, establish multivariabl...

For 1 ≤ p < ∞ let Cp denote the usual von Neumann-Schatten ideal of compact operators on 2. The standard basis of Cp is a conditional one and so it is of interest to be able to identify the sets of coordinates for which the corresponding projection is bounded. In this paper we survey and extend the known classes of bounded projections of this type. In particular we show that some recent results...

An improvement of a bound of Yankosky (2003) is presented in this paper, thanks to a restriction which has been recently obtained by the authors on the Schur multiplier M(L) of a finite dimensional nilpotent Lie algebra L. It is also described the structure of all nilpotent Lie algebras such that the bound is attained. An important role is played by the presence of a derived subalgebra of maxim...

This paper details the diassociative analogue of results concerning Schur multiplier and other extension-theoretic concepts that originate in group theory. We first prove covers algebras are unique. Second, we show a algebra is characterized by second cohomology with coefficients field. Third, establish criteria for when center cover maps onto algebra. Along way, obtain collection exact sequenc...

For a fixed characteristic p and a fixed simple group G, various bicyclic extensions m.G.a may occur, where G.a is a subgroup of the automorphism group of G and m is a cyclic factor of the Schur multiplier of G.a. For each such group G.a, the information about all bicyclic extensions m.G.a that occur in the ATLAS of Finite Groups is shown together in one document. Each file starts with the name...

An improvement of a bound of Yankosky (2003) is presented in this paper, thanks to a restriction which has been recently obtained by the authors on the Schur multiplier M(L) of a finite dimensional nilpotent Lie algebra L. It is also described the structure of all nilpotent Lie algebras such that the bound is attained. An important role is played by the presence of a derived subalgebra of maxim...