Abstract Let ( X , J ) be a nilmanifold with an invariant nilpotent complex structure. We study the existence of p -Kähler structures (which include Kähler and balanced metrics) on . More precisely, we determine optimal such that there are no Finally, show that, contrarily to case, compact manifolds is relation between metrics degeneracy step Frölicher spectral sequence. can arbitrarily large.

In this paper, we give some new characterizations of finite p-nilpotent groups by using the notion of HC-subgroups and extend several recent results. Mathematics Subject Classification (2010). 20D10, 20D20.

Abstract Let p be a prime and let G finite group such that the smallest divides | is . We find sharp bounds, depending on , for commuting probability average character degree to guarantee nilpotent or supersolvable.

We study multipliers on graded nilpotent Lie groups defined via group Fourier transform. More precisely, we show that Hörmander-type conditions the imply $L^p$-boundedness. express these using difference operators and

we call $h$ an $ss$-embedded subgroup of $g$ if there exists a‎ ‎normal subgroup $t$ of $g$ such that $ht$ is subnormal in $g$ and‎ ‎$hcap tleq h_{sg}$‎, ‎where $h_{sg}$ is the maximal $s$-permutable‎ ‎subgroup of $g$ contained in $h$‎. ‎in this paper‎, ‎we investigate the‎ ‎influence of some $ss$-embedded subgroups on the structure of a‎ ‎finite group $g$‎. ‎some new results were obtained.‎

Let P be a Poisson algebra with Lie bracket {,} over field F of characteristic p≥0. In this paper, the structure is investigated. particular, if solvable respect to its bracket, then we prove that ideal J generated by all elements {{{x1,x2},{x3,x4}},x5} x1,…,x5∈P associative nilpotent index bounded function derived length P. We use result further and p≠2, {P,P}P nil.

We exhibit pseudo Riemannian manifolds which are Szabó nilpotent of arbitrary order, or which are Osserman nilpotent of arbitrary order, or which are Ivanov-Petrova nilpotent of order 3.

Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = {0neq x in R | xy in N(R) for some y in R^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in N(R)$, or equivalently, $yx in N(R)$, where $N(R)$ denoted the nilpotent elements of $R$. Recently, it has been proved that if $R$ is a left A...