In string theory, nilpotence of the BRS operator δ for the string functional relates the Chern-Simons term in the gauge-invariant antisymmetric tensor field strength to the central term in the Kac-Moody algebra. We generalize these ideas to p-branes with odd p and find that the Kac-Moody algebra for the string becomes the Mickelsson-Faddeev algebra for the p-brane.

We study the combinatorics of ad-nilpotent ideals of a Borel subalgebra of sl(n+1,C). We provide an inductive method for calculating the class of nilpotence of these ideals and formulas for the number of ideals having a given class of nilpotence. We study the relationships between these results and the combinatorics of Dyck paths, based upon a remarkable bijection between ad-nilpotent ideals an...

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.

Suppose that we are given a set S of powers of a prime p and that 1 ∈ S. A technique is presented that enables the construction of a p-group of specified nilpotence class n such that its set of irreducible character degrees is exactly S. If |S| ≥ 2, then this can be done for 2 ≤ n ≤ p and if p ∈ S, then the only requirement is 2 ≤ n.

In this paper we show that any finite algebra A satisfying a weak left nilpotence condition has the property that all maximal subuniverses are congruence blocks. Conversely, if every subalgebra of A has the property that all maximal subuniverses are congruence blocks, then A satisfies the aforementioned nilpotence condition.