In his paper mentioned in the title, which appears in the same issue of this journal, Mehdi Radjabalipour derives the cyclic decomposition of an algebraic linear transformation. A more general structure theory for linear transformations appears in Irving Kaplansky's lovely 1954 book on infinite abelian groups. We present a translation of Kaplansky's results for abelian groups into the terminolo...

A group is called morphic if for each normal endomorphism α in end(G),there exists β such that ker(α)= Gβ and Gα= ker(β). In this paper, we consider the case that there exist normal endomorphisms β and γ such that ker(α)= Gβ and Gα = ker(γ). We call G quasi-morphic, if this happens for any normal endomorphism α in end(G). We get the following results: G is quasi-morphic if and only if, for any ...

We study the Dirac propagator dressed by an arbitrary number N of photons means a worldline approach, which makes use supersymmetric N=1 spinning particle model on line, coupled to external Abelian vector field. obtain compact off-shell master formula for tree level scattering amplitudes associated propagator. In particular, unlike in other approaches, we express fermionic degrees freedom using...

a $p$-group $g$ is $p$-central if $g^{p}le z(g)$‎, ‎and $g$ is‎ ‎$p^{2}$-abelian if $(xy)^{p^{2}}=x^{p^{2}}y^{p^{2}}$ for all $x,yin‎ ‎g$‎. ‎we prove that for $g$ a finite $p^{2}$-abelian $p$-central ‎$p$-group‎, ‎excluding certain cases‎, ‎the order of $g$ divides the ‎order of $text{aut}(g)$‎.

Hidden in the expansion of the Kontsevich integral, graded by loops rather than by degree, is a new notion of finite type invariants of knots, closely related to S-equivalence, and with respect to which the Kontsevich integral is the universal finite type invariant, modulo S-equivalence. In addition, the 2-loop part Q of the Kontsevich integral behaves like an equivariant version of Casson’s in...

It is known that the Pak-Stanley labeling of the Shi hyperplane arrangement provides a bijection between the regions of the arrangement and parking functions. For any graph G, we define the G-semiorder arrangement and show that the Pak-Stanley labeling of its regions produces all G-parking functions. In his study of Kazhdan-Lusztig cells of the affine Weyl group of typeAn−1, [10], J.-Y. Shi int...