A characterization of those automata that structurally generate finite groups

Antonenko and Russyev independently have shown that any Mealy automaton with no cycles with exit--that is, where every cycle in the underlying directed graph is a sink component--generates a fi- nite (semi)group, regardless of the choice of the production functions. Antonenko has proved that this constitutes a characterization in the non-invertible case and asked for the invertible case, which is proved in this paper

Branch Rings, Thinned Rings, Tree Enveloping Rings

We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees. In particular, for every field k we construct a k-algebra K which (1) is finitely generated and infinite-dimensional, but has only finite-dimensional quotients; (2) has a subalgebra of finite codimension, isomorphic to $M_2(K)$; (3) is prime; (4) has quadratic growth, and therefore Gelfand-Kirillov dimension 2; (5) is recursively presented; (6) satisfies no identity; (7) contains a transcendental, invertible element; (8) is semiprimitive if k has characteristic $\neq2$; (9) is graded if k has characteristic 2; (10) is primitive if k is a non-algebraic extension of GF(2); (11) is graded nil and Jacobson radical if k is an algebraic extension of GF(2).Comment: 35 pages; small changes wrt previous versio

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

A Sulfhydryl-Reactive Ruthenium (II) Complex and Its Conjugation to Protein G as a Universal Reagent for Fluorescent Immunoassays

To develop a fluorescent ruthenium complex for biosensing, we synthesized a novel sulfhydryl-reactive compound, 4-bromophenanthroline bis-2,2′-dipyridine Ruthenium bis (hexafluorophosphate). The synthesized Ru(II) complex was crosslinked with thiol-modified protein G to form a universal reagent for fluorescent immunoassays. The resulting Ru(II)-protein G conjugates were identified by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE). The emission peak wavelength of the Ru(II)-protein G conjugate was 602 nm at the excitation of 452 nm which is similar to the spectra of the Ru(II) complex, indicating that Ru(II)-protein G conjugates still remain the same fluorescence after conjugation. To test the usefulness of the conjugate for biosensing, immunoglobulin G (IgG) binding assay was conducted. The result showed that Ru(II)-protein G conjugates were capable of binding IgG and the more cross-linkers to modify protein G, the higher conjugation efficiency. To demonstrate the feasibility of Ru(II)-protein G conjugates for fluorescent immunoassays, the detection of recombinant histidine-tagged protein using the conjugates and anti-histidine antibody was developed. The results showed that the histidine-tagged protein was successfully detected with dose-response, indicating that Ru(II)-protein G conjugate is a useful universal fluorescent reagent for quantitative immunoassays

On Cubic Representations of SL(2,Aug(Z2Cp)) in Characteristic Two

AbstractLet R = Aug(Z2Cp) be the augmentation ideal of the group ring Z2Cp of the cyclic group Cp of order an odd prime p, α a primitive pth root of unity over Z2, F = Z2[α], α* an element in R of multiplicative order p, and [formula]. Any F-representations, finite or infinite dimensional, of SL(2, R) where A satisfies (x − α)(x − α−1)(x − 1) = 0, is shown to be equivalent to one into an F-algebra of the form [formula], where A is an F-algebra of dimension at most 6, B is an F-algebra of dimension at most 4, and M, N, are bimodules of dimension at most 4

On pairs of matrices generating matrix rings and their presentations

AbstractLet Mn(Z) be the ring of n-by-n matrices with integral entries, and n⩾2. This paper studies the set Gn(Z) of pairs (A,B)∈Mn(Z)2 generating Mn(Z) as a ring. We use several presentations of Mn(Z) with generators X=∑i=1nEi+1,i and Y=E11 to obtain the following consequences.(1)Let k⩾1. The following rings have presentations with 2 generators and finitely many relations:(a)⊕j=1kMmj(Q) for any m1,…,mk⩾2.(b)⊕j=1kMnj(Z), where n1,…,nk⩾2, and the same ni is repeated no more than three times.(2)Let D be a commutative domain of sufficiently large characteristic over which every finitely generated projective module is free. We use 4 relations for X and Y to describe all representations of the ring Mn(D) into Mm(D) for m⩾n.(3)We obtain information about the asymptotic density of Gn(F) in Mn(F)2 over different fields, and over the integers

THE GROUP OF AUTOMORPHISMS OF A 3-GENERATED 2-GROUP OF INTERMEDIATE GROWTH

We decidate this paper to John Rhodes on his 65th birthday. Abstract. The automorphism group of a 3-generated 2-group G of intermediate growth is determined and it is shown that the outer group of automorphisms of G to be an elementary abelian 3- group of infinite rank. 1