Two groups are said to have the same nilpotent genus if they have the same nilpotent quotients. We answer four questions of Baumslag concerning nilpotent completions. (i) There exists a pair of finitely generated, residually torsion-free-nilpotent groups of the same nilpotent genus such that one is finitely presented and the other is not. (ii) There exists a pair of finitely presented, residual...

Let F be a p-adic field and let G connected reductive group defined over F. We assume p is large. Denote g the Lie algebra of G. To each vertex s reduced Bruhat–Tits’ building G, we associate as usual gs residual Fq. normalize suitably Fourier-transform f↦fˆ on Cc∞(g(F)). study subspace functions f∈Cc∞(g(F)) such that orbital integrals f fˆ are 0 for element g(F) which not topologically nilpote...

this work is a continuation of [a‎. ‎o‎. ‎asar‎, ‎‎‎on infinitely generated groups whose proper subgroups are solvable‎, ‎{em j‎. ‎algebra}‎, ‎{bf 399} (2014) 870-886.]‎, ‎where it was shown‎ ‎that a perfect infinitely generated group whose proper subgroups‎ are solvable and in whose homomorphic images normal closures of ‎finitely generated subgroups are residually nilpotent is a fitting‎‎$p$-g...

We associate a graph NG with a group G (called the non-nilpotent graph of G) as follows: take G as the vertex set and two vertices are adjacent if they generate a non-nilpotent subgroup. In this paper we study the graph theoretical properties of NG and its induced subgraph on G\nil(G), where nil(G) = {x ∈ G | 〈x, y〉 is nilpotent for all y ∈ G}. For any finite group G, we prove that NG has eithe...

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

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.

For a $p$-group of order $p^n$, it is known that the $2$-nilpotent multiplier equal to $|\mathcal{M}^{(2)}(G)|=p^{\f12n(n-1)(n-2)+3-s_2(G)}$ for an integer $s_2(G)$. In this article, we characterize all non abelian $p$-groups satisfying in $s_2(G)\in\{1,2,3\}.

Let G be a connected reductive linear algebraic group defined over an algebraically closed field of characteristic p. Assume that p is good for G. In this note we classify all the spherical nilpotent G-orbits in the Lie algebra of G. The classification is the same as in the characteristic zero case obtained by D.I. Panyushev in 1994, [32]: for e a nilpotent element in the Lie algebra of G, the ...

Let G be a multiplicatively written p-separable abelian group and R a commutative unitary ring of prime characteristic p so that Rp i has nilpotent elements for each positive integer i > 1. Then, we prove that, the normed unit p-subgroup S(RG) of the group ring RG is quasi-complete if and only if G is a bounded p-group. This strengthens our recent results in (Internat. J. Math. Analysis, 2006) ...