Generic expansion of an abelian variety by a subgroup

On the p-adic closure of a subgroup of rational points on an Abelian variety

In 2007, B. Poonen (unpublished) studied the p–adic closure of a subgroup of rational points on a commutative algebraic group. More recently, J. Belläıche asked the same question for the special case of Abelian varieties. These problems are p–adic analogues of a question raised earlier by B. Mazur on the density of rational points for the real topology. For a simple Abelian variety over the fie...

On the Quotient Variety of an Abelian Variety.

On $m^{th}$-autocommutator subgroup of finite abelian groups

Let $G$ be a group and $Aut(G)$ be the group of automorphisms of‎ ‎$G$‎. ‎For any natural‎ number $m$‎, ‎the $m^{th}$-autocommutator subgroup of $G$ is defined‎ ‎as‎: ‎$$K_{m} (G)=langle[g,alpha_{1},ldots,alpha_{m}] |gin G‎,‎alpha_{1},ldots,alpha_{m}in Aut(G)rangle.$$‎ ‎In this paper‎, ‎we obtain the $m^{th}$-autocommutator subgroup of‎ ‎all finite abelian groups‎.

Algebraic Cycles on an Abelian Variety

It is shown that to every Q-linear cycle α modulo numerical equivalence on an abelian variety A there is canonically associated a Q-linear cycle α modulo rational equivalence on A lying above α, characterised by a condition on the spaces of cycles generated by α on products of A with itself. The assignment α 7→ α respects the algebraic operations and pullback and push forward along homomorphism...

subgroup intersection graph of finite abelian groups

let $g$ be a finite group with the identity $e$‎. ‎the subgroup intersection graph $gamma_{si}(g)$ of $g$ is the graph with vertex set $v(gamma_{si}(g)) = g-e$ and two distinct vertices $x$ and $y$ are adjacent in $gamma_{si}(g)$ if and only if $|leftlangle xrightrangle capleftlangle yrightrangle|>1$‎, ‎where $leftlangle xrightrangle $ is the cyclic subgroup of $g$ generated by $xin g$‎. ‎in th...