in this paper we give some general results on the non-splitextension group $overline{g}_{n} = 2^{2n}{^{cdot}}sp(2n,2), ngeq2.$ we then focus on the group $overline{g}_{4} =2^{8}{^{cdot}}sp(8,2).$ we construct $overline{g}_{4}$ as apermutation group acting on 512 points. the conjugacy classes aredetermined using the coset analysis technique. then we determine theinertia factor groups and fischer...

Let (G, u) be an Archimedean norm-complete dimension group with order-unit. Continuing a previous paper, we study intervals (i.e., nonempty upward directed lower subsets) of G which are closed with respect to the canonical norm of (G, u). In particular, we establish a canonical one-to-one correspondence between closed intervals of G and certain affine lower semicontinuous functions on the state...

If a finite group G has a presentation with d generators and r relations, it is well-known that r−d is at least the rank of the Schur multiplier of G; a presentation is called efficient if equality holds. There is an analogous definition for proficient profinite presentations. We show that many perfect groups have proficient presentations. Moreover, we prove that infinitely many alternating gro...

In this note, we announce some results about the Schur multipliers of the known finite simple groups. Proofs will appear elsewhere. We shall conclude with a summary of current knowledge on the subject. Basic properties of multipliers and covering groups of finite groups are discussed in [6]. Notation for groups of Lie type is standard [3], [8]. G' denotes the commutator subgroup of the group G,...

A locally compact group G is discrete if and only the Fourier algebra A(G) has a non-zero (weakly) multiplier. We partially extend this result to setting of ultraspherical hypergroups. Let H be an hypergroup let A(H) denote corresponding algebra. will give several characterizations discreteness in terms algebraic properties A(H). also study Arens regularity closed ideals

Given a group G and an integer n ≥ 2 we construct a new group e K(G, n). Although this construction naturally occurs in the context of finding new invariants for complex algebraic surfaces, it is related to the theory of central extensions and the Schur multiplier. A surprising application is that Abelian groups of odd order possess naturally defined covers that can be computed from a given cov...

A semidiscrete multiplier is an operator between a space of functions or distributions on a locally compact Abelian group G on the one hand, and a space of sequences on a discrete subgroup H of G on the other hand, with the property that it commutes with shifts by H. We describe the basic form of such operators and show a number of representation theorems for classical spaces like Lp, C0, etc. ...

Abstract Let $$\Gamma &lt; G$$ Γ &lt; G be a discrete subgroup of locally compact unimodular group G . $$m\in C_b(G)$$ m ∈ C b ( )</mml:m...

| A convex upper bound of the mixed structured singular value is analyzed. The upper bound is based on a multiplier method. It is simple, it can exploit low-rank properties and it is shown to be less conservative than the well-known (D; G)-scaling. A direct relationship with (D; G)-scaling is given. The upper bound can be modiied to one that is continuous with an explicit Lipschitz constant. Ke...