Let G be the symmetric group of degree n. ω(G) maximal size a subset S such that 〈x,y〉=G whenever x,y∈S and x≠y let σ(G) minimal family proper subgroups whose union is G. We prove both functions are asymptotically equal to 12(nn/2) when n even. This, together with result S. Blackburn, implies σ(G)/ω(G) tends 1 as n→∞. Moreover, we give lower bound n/5 on which independent classification finite ...

We investigated maximal Prym varieties on finite fields by attaining their upper bounds on the number of rational points. This concept gave us a motivation for defining a generalized definition of maximal curves i.e. maximal morphisms. By MAGMA, we give some non-trivial examples of maximal morphisms that results in non-trivial examples of maximal Prym varieties.

Most morphological operators use a unique structuring element, possibly at different scales, to describe an object. In addition, morphological algorithms are often restricted to 1D structuring elements, combinations of 1D elements, or isotropic structuring elements (like circles), because of the lack of methods directly applicable to arbitrary shaped 2D structuring elements. While these descrip...

the aim of this paper is to study semigroups possessing $e$-regular elements, where an element $a$ of a semigroup $s$ is {em $e$-regular} if $a$ has an inverse $a^circ$ such that $aa^circ,a^circ a$ lie in $ esubseteq e(s)$. where $s$ possesses `enough' (in a precisely defined way) $e$-regular elements, analogues of green's lemmas and even of green's theorem hold, where green's relations $mbox{$...

Let L = L1 × · · · × Ln be the product of n lattices, each of which has a bounded width. Given a subset A ⊆ L, we show that the problem of extending a given partial list of maximal independent elements of A in L can be solved in quasi-polynomial time. This result implies, in particular, that the problem of generating all minimal infrequent elements for a database with semi-lattice attributes, a...

We provide the first necessary and sufficient conditions in the literature for the existence of maximal elements in a non-binary choice framework. As an application, the characterization of the existence of maximal elements for acyclic binary relations obtained in Rodŕıguez-Palmero and Garćıa-Lapresta, 2002, Mathematical Social Sciences 43, 55-60, is deduced as a Corollary. Further characteriza...

the aim of this paper is to study semigroups possessing $e$-regular elements, where an element $a$ of a semigroup $s$ is {em $e$-regular} if $a$ has an inverse $a^circ$ such that $aa^circ,a^circ a$ lie in $ esubseteq e(s)$. where $s$ possesses `enough' (in a precisely defined way) $e$-regular elements, analogues of green's lemmas and even of green's theorem hold, where green&apos...