As a corollary of work of Ozsváth and Szabó, it is shown that the classical concordance group of algebraically slice knots has an infinite cyclic summand and in particular is not a divisible group. Let A denote the concordance group of algebraically slice knots, the kernel of Levine’s homomorphism φ : C → G, where C is the classical knot concordance group and G is Levine’s algebraic concordance...

Example 1 Lets consider the integers from 1 to 10,000. The properties are defined as follows: E1 = property that an integer is divisible by 4 E2 = property that an integer is divisible by 5 E3 = property that an integer is divisible by 6 The probabilities of individual divisability are easily computed: Pr [E1] = probability the number is divisible by 4 = 1=4 Pr [E2] = probability the number is ...

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...

a subgroup $h$ is said to be $nc$-supplemented in a group $g$ if there exists a subgroup $kleq g$ such that $hklhd g$ and $hcap k$ is contained in $h_{g}$, the core of $h$ in $g$. we characterize the supersolubility of finite groups $g$ with that every maximal subgroup of the sylow subgroups is $nc$-supplemented in $g$.

suppose that $h$ is a subgroup of $g$‎, ‎then $h$ is said to be‎ ‎$s$-permutable in $g$‎, ‎if $h$ permutes with every sylow subgroup of‎ ‎$g$‎. ‎if $hp=ph$ hold for every sylow subgroup $p$ of $g$ with $(|p|‎, ‎|h|)=1$)‎, ‎then $h$ is called an $s$-semipermutable subgroup of $g$‎. ‎in this paper‎, ‎we say that $h$ is partially $s$-embedded in $g$ if‎ ‎$g$ has a normal subgroup $t$ such that $ht...

Let $ G$ be a finite group and $p$ prime. \mathrm{Vo}(G) denote the set of orders vanishing elements, $\mathrm{Vo}_{p} (G)$ subset consisting those elements divisible by $\mathrm{Vo}_{p'} (G) not $p$. Dolfi, Pacifi, Sanus Spiga proved that if is p $-power for all a\in \mathrm{Vo}(G)$, then G has normal Sylow $-subgroup. In another article, same authors also show \mathrm{Vo}_{p'}(G) =\emptyset $...

Divisible design digraphs are constructed from skew balanced generalized weighing matrices and Hadamard matrices. Commutative non-commutative association schemes shown to be attached the divisible digraphs.

The algebraic structure of divisible abelian semigroups has been studied in [9] and [l]. Some results on the topological and algebraic structure of compact uniquely divisible abelian semigroups have been obtained in [4] and [5]. A statement of equivalent conditions for a compact abelian semigroup to be divisible is presented in the present paper. Some of the results in [4] are extended to subun...

We introduce the concept of a (p; d)-divisible problem, where p reeects the number of processors and d the number of communication phases of a parallel algorithm solving the problem. We call problems that are recursively (n ; O(1))-divisible in a work-optimal way with 0 < < 1 ideally divisible and give motivation drawn from parallel computing for the relevance of that concept. We show that seve...