NILPOTENT p-LOCAL FINITE GROUPS

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup

Classifying Finite 2-nilpotent P-groups, Lie Algebras and Graphs: Equivalent Wild Problems

We reduce the graph isomorphism problem to 2-nilpotent p-groups isomorphism problem (and to finite 2-nilpotent Lie algebras the ring Z/pZ. Furthermore, we show that classifying problems in categories graphs, finite 2-nilpotent p-groups, and 2-nilpotent Lie algebras over Z/pZ are polynomially equivalent and wild.

On a conjecture of a bound for the exponent of the Schur multiplier of a finite $p$-group

Let $G$ be a $p$-group of nilpotency class $k$ with finite exponent $exp(G)$ and let $m=lfloorlog_pk floor$. We show that $exp(M^{(c)}(G))$ divides $exp(G)p^{m(k-1)}$, for all $cgeq1$, where $M^{(c)}(G)$ denotes the c-nilpotent multiplier of $G$. This implies that $exp( M(G))$ divides $exp(G)$, for all finite $p$-groups of class at most $p-1$. Moreover, we show that our result is an improvement...

Local Functional Equations for Submodule Zeta Functions Associated to Nilpotent Algebras of Endomorphisms

We give a sufficient criterion for generic local functional equations for submodule zeta functions associated to nilpotent algebras of endomorphisms defined over number fields. This allows us, in particular, to prove various conjectures on such functional equations for ideal zeta functions of nilpotent Lie lattices. Via the Mal’cev correspondence, these results have corollaries pertaining to ze...

Harmonic analysis on finite Heisenberg groups

This paper contains some new results on harmonic analysis on finite Heisenberg groups. We compute the dual and obtain further consequences, not restricting ourselves to finite fields or to finite local rings. We give an outlook on harmonic analysis on special finite nilpotent groups of class 3. We also recall the use of nilpotent groups in various areas of mathematics and mathematical physics.