In this paper, we establish a strategy for the calculation of proportion everywhere locally soluble diagonal hypersurfaces [Formula: see text] fixed degree. Our is based on product formula established by Bright, Browning and Loughran. Their reduces problem into proportions text]-soluble all places text]. As worked examples, carry out our in cases quadratic cubic hypersurfaces. consequence, prov...

Abstract The aim of this paper is to provide a contribution the theory uncountable groups and that paranilpotent groups. Extending structural results in Franciosi de Giovanni (Ricerche Mat 40:321–333, 1991) et al. (Comm Algebra 49:3020–3033, 2021), we prove locally soluble minimal non-paranilpotent , i.e. whose proper subgroups are paranilpotent, soluble. It also shown class countably recogniza...

In this paper we study some locally soluble FC-groups G all of whose factor-groups G/N are residually finite.

Abstract The structure of locally soluble periodic groups in which every abelian subgroup is cyclic was described over 20 years ago. We complete the aforementioned characterization by dealing with non-periodic case. also describe finite all subgroups are cyclic.

The c-dimension of a group is the maximum length of a chain of nested centralizers. It is proved that a periodic locally soluble group of finite cdimension k is soluble of derived length bounded in terms of k, and the rank of its quotient by the Hirsch–Plotkin radical is bounded in terms of k. Corollary: a pseudo-(finite soluble) group of finite c-dimension k is soluble of derived length bounde...

Abstract Sesbania grandiflora leaves are extensively used locally since ancient time as in traditional systems. Base on mainly folkloric use, we investigated to know the potential of Sesbania grandiflora leaves extracts through biological works in vivo and in vitro. The ethanolic extract of S. grandiflora leaves was partitioned into ethyl acetate soluble fraction (ESF), petroleum ether so...

the author studies the $bf r$$g$-module $a$ such that $bf r$ is an associative ring‎, ‎a group $g$ has infinite section $p$-rank (or infinite 0-rank)‎, ‎$c_{g}(a)=1$‎, ‎and for every‎ ‎proper subgroup $h$ of infinite section $p$-rank (or infinite 0-rank respectively) the quotient module $a/c_{a}(h)$ is‎ ‎a finite $bf r$-module‎. ‎it is proved that if the group $g$ under‎ ‎consideration is local...

abstract sesbania grandiflora leaves are extensively used locally since ancient time as in traditional systems. base on mainly folkloric use, we investigated to know the potential of sesbania grandiflora leaves extracts through biological works in vivo and in vitro. the ethanolic extract of s. grandiflora leaves was partitioned into ethyl acetate soluble fraction (esf), petroleum ether soluble ...

We prove that a positive proportion of hypersurfaces in products projective spaces over $${\mathbb {Q}}$$ are everywhere locally soluble, for almost all multidegrees and dimensions, as generalization theorem Poonen Voloch [25]. also study the specific case genus 1 curves {P}}^1 \times {\mathbb {P}}^1$$ defined , represented bidegree (2, 2)-forms, show soluble such is approximately $$87.4\%$$ . ...