We consider a cyclic group of order p acting on a module incharacteristic p and show how to reduce the calculation of the symmetric algebra to that of the exterior algebra. Consider a cyclic group of order p acting on a polynomial ring S = k[x1, . . . , xr], where k is a field of characteristic p; this is equivalent to the symmetric algebra S∗(V ) on the module V generated by x1, . . . , xr. We...

The Wronski map is a finite, PGL2(C)-equivariant morphism from the Grassmannian Gr(d, n) to a projective space (the projectivization of a vector space of polynomials). We consider the following problem. If Cr ⊂ PGL2(C) is a cyclic subgroup of order r, how may Cr-fixed points are in the fibre of the Wronski map over a Cr-fixed point in the base? In this paper, we compute a general answer in term...

We associate a graph ΓG to a non locally cyclic group G (called the non-cyclic graph of G) as follows: take G\Cyc(G) as vertex set, where Cyc(G) = {x ∈ G | 〈x, y〉 is cyclic for all y ∈ G}, and join two vertices if they do not generate a cyclic subgroup. We study the properties of this graph and we establish some graph theoretical properties (such as regularity) of this graph in terms of the gro...

We associate a graph CG to a non locally cyclic group G (called the non-cyclic graph of G) as follows: take G\Cyc(G) as vertex set, where Cyc(G) = {x ∈ G | 〈x, y〉 is cyclic for all y ∈ G} is called the cyclicizer of G, and join two vertices if they do not generate a cyclic subgroup. For a simple graph Γ, w(Γ) denotes the clique number of Γ, which is the maximum size (if it exists) of a complete...

In Crisp environment, the notion of cyclic group on a set is well known. We study an extension of this classical notion to the Mfuzzy sets to define the concept of Mcyclic fuzzy groups. By using these cyclic ,M-fuzzy groups, we then define cyclic M-fuzzy group family and investigate its structure properties with applications. 2000AMS Subject classification: 08A72 , 20N25, 03E72, 94D05

Suppose G is a finite cyclic group and M a closed smooth G–manifold. In this paper we will show that there is a nonsingular real algebraic G–variety X which is equivariantly diffeomorphic to M and all G–vector bundles over X are strongly algebraic.

This paper presents a new algorithm for distributed garbage collection and outlines its implementation within the Network Objects system. The algorithm is based on a reference listing scheme augmented by partial tracing in order to collect distributed garbage cycles. Our collector is designed to be flexible thereby allowing efficiency, expediency and fault-tolerance to be traded against complet...

We prove that the amalgamated product of free groups with cyclic amalgamations satisfying certain conditions are virtually free-by-cyclic. In case the cyclic amalgamated subgroups lie outside the derived group such groups are free-by-cyclic. Similarly a one-relator HNN-extension in which the conjugated elements either coincide or are independent modulo the derived group is shown to be free-by-c...

A subset X of an abelian G is said to be complete if every element of the subgroup generated by X can be expressed as a nonempty sum of distinct elements from X . Let A ⊂ Zn be such that all the elements of A are coprime with n. Solving a conjecture of Erdős and Heilbronn, Olson proved that A is complete if n is a prime and if |A| > 2√n. Recently Vu proved that there is an absolute constant c, ...