Let k be a perfect field of characteristic p ≥ 3. Let X be a non-supersingular K3 surface over k, and Ψ the enlarged formal Brauer group associated to X . We consider the deformation space of X . In this note, we show that the local moduli space M◦◦ of X with trivial associated deformation of Ψ admits a natural p-divisible formal group structure.

A topological group G is said to be almost maximally almost-periodic if its von Neumann radical n(G) is non-trivial, but finite. In this paper, we prove that (a) every countably infinite abelian torsion group, (b) every abelian torsion group of cardinality greater than continuum, and (c) every (non-trivial) divisible abelian torsion group admits a (Hausdorff) almost maximally almost-periodic gr...

Abstract Let denote the maximal number of different primes that may occur in order a finite solvable group G , all elements which have orders divisible by at most n distinct primes. We show for . As an application, we improve on recent bound Hung and Yang arbitrary groups.

Let Kq(n, w, t, d) be the minimum size of a code over Zq of length n, constant weight w, such that every word with weight t is within Hamming distance d of at least one codeword. In this article, we determine Kq(n, 4, 3, 1) for all n ≥ 4, q = 3, 4 or q = 2m + 1 with m ≥ 2, leaving the only case (q, n) = (3, 5) in doubt. Our construction method is mainly based on the auxiliary designs, H-frames,...

Let Λ be some class of Abelian groups. We say that a group A ∈ is determined by its endomorphism semigroup E⋆(A) in if the isomorphism ≅ E⋆(B), where B Λ, implies B. describe split groups $$ {\mathcal{QD}}_{\mathrm{cd}} completely decomposable quotient divisible their semigroups .

We investigate the existence of group divisible designs (GDDs) with block size three, group-type gw and index λ. We prove that the elementary necessary conditions for the existence of such a GDD are also sufficient, which generalizes the result of Colbourn, Hoffman and Rees.

Recently, some divisible electronic cash (e-cash) systems have been proposed. However, in existing divisible e-cash systems, efficiency or unlinkability is not sufficiently accomplished. In the existing efficient divisible cash systems, all protocols are conducted in the order of the polynomial of logN where N is the divisibility precision (i.e., (the total coin amount)/ (minimum divisible unit...

We introduce a new technique for constructing pairwise balanced designs and group divisible designs from finite groups. These constructed designs do not give designs with new parameters but our construction gives rise to designs having a transitive automorphism group that also preserves the resolution classes.

Consider a gain graph with abelian gain group having no odd torsion. If there is a binary cycle basis each of whose members can be lifted to a closed walk whose gain is the identity, then the gain graph is balanced, provided that the graph is finite or the group has no nontrivial infinitely 2-divisible elements.

Let N be a closed, connected, smooth 4-manifold with H1(N ;Z) = 0. Our main result is the following classification of the set E(N) of smooth embeddings N → R up to smooth isotopy. Haefliger proved that the set E(S) with the connected sum operation is a group isomorphic to Z12. This group acts on E(N) by embedded connected sum. Boéchat and Haefliger constructed an invariant BH : E(N) → H2(N ;Z) ...