$$2$$ 2 -Nilpotent real section conjecture

on huppert's conjecture for f_4(2)

let $g$ be a finite group and let $text{cd}(g)$ be the set of all‎ ‎complex irreducible character degrees of $g$‎. ‎b‎. ‎huppert conjectured‎ ‎that if $h$ is a finite nonabelian simple group such that‎ ‎$text{cd}(g) =text{cd}(h)$‎, ‎then $gcong h times a$‎, ‎where $a$ is‎ ‎an abelian group‎. ‎in this paper‎, ‎we verify the conjecture for‎ ${f_4(2)}.$‎

Jacobian Conjecture and Nilpotent Mappings

We prove the equivalence of the Jacobian Conjecture (JC(n)) and the Conjecture on the cardinality of the set of fixed points of a polynomial nilpotent mapping (JN(n)) and prove a series of assertions confirming JN(n).

A Refinement of the Toral Rank Conjecture for 2-step Nilpotent Lie Algebras

It is known that the total (co)-homoloy of a 2-step nilpotent Lie algebra g is at least 2|z|, where z is the center of g. We improve this result by showing that a better lower bound is 2t, where t = |z|+ [ |v|+1 2 ] and v is a complement of z in g. Furthermore, we provide evidence that this is the best possible bound of the form 2t.

-λ coloring of graphs and Conjecture Δ ^ 2

For a given graph G, the square of G, denoted by G2, is a graph with the vertex set V(G) such that two vertices are adjacent if and only if the distance of these vertices in G is at most two. A graph G is called squared if there exists some graph H such that G= H2. A function f:V(G) {0,1,2…, k} is called a coloring of G if for every pair of vertices x,yV(G) with d(x,y)=1 we have |f(x)-f(y)|2 an...

Section 2