Weakly minimal groups with a new predicate

finite groups whose minimal subgroups are weakly h*-subgroups

let $g$ be a finite group‎. ‎a subgroup‎ ‎$h$ of $g$ is called an $mathcal h $ -subgroup in‎ ‎$g$ if $n_g (h)cap h^gleq h$ for all $gin‎ ‎g$. a subgroup $h$ of $g$ is called a weakly‎ $mathcal h^ast $-subgroup in $g$ if there exists a‎ ‎subgroup $k$ of $g$ such that $g=hk$ and $hcap‎ ‎k$ is an $mathcal h$-subgroup in $g$. we‎ ‎investigate the structure of the finite group $g$ under the‎ ‎assump...

On Weakly O-minimal Non-valuational Expansions of Ordered Groups

Let M = 〈M,<,+, . . .〉 be a weakly o-minimal expansion of an ordered group. This paper has two parts. In the rst part, we introduce the notion of M having no external limits and use it to prove that a large collection of non-valuational structures M do not admit de nable Skolem functions. In the second part, we provide an alternative characterization of the canonical o-minimal completion from [...

Predicate-Induced Permutation Groups

Natural languages abound in combinatorial phenomena that are related to the predicate of the sentence and its ability to permute noun phrase arguments. After compiling several illustrative phenomena of natural languages, I propose a novel analysis in terms of permutation groups, a concept borrowed from mathematical combinatorics that is ubiquitous in applied sciences. I show that each natural l...

Digital cohomology groups of certain minimal surfaces

In this study, we compute simplicial cohomology groups with different coefficients of a connected sum of certain minimal simple surfaces by using the universal coefficient theorem for cohomology groups. The method used in this paper is a different way to compute digital cohomology groups of minimal simple surfaces. We also prove some theorems related to degree properties of a map on digital sph...

Stable Theories with A New Predicate