A nilpotent quotient algorithm for graded Lie rings of prime characteristic is described. The algorithm has been implemented and applications have been made to the investigation of the associated Lie rings of Burnside groups. New results about Lie rings and Burnside groups are presented. These include detailed information on groups of exponent 5 and 7 and their associated Lie rings. Appeared: J...

In this article two somewhat distinct methods are used to study the properties of groups whose orders are powers of a prime. What may, for the purpose of distinction, be called the usual method is applied in the first part to establish certain properties of the commutators of a group. The commutators are differentiated among themselves by the introduction of the notion of successive commutators...

Given a $p$-group $G$ and subgroup-closed class $\mathfrak{X}$, we associate with each $\mathfrak{X}$-subgroup $H$ certain quantities which count $\mathfrak{X}$-subgroups containing subject to further properties. We show in Theorem I that one of the said is always $\equiv 1 \pmod p$ if only same holds for others. In II supplement above result by focusing on normal III obtain sharpened version c...

This paper provides a critical analysis of the growth regressions in Burnside and Dollar (2000). First, we analyze the relation between aid and government expenditure in a modified neoclassical growth model. We find that while good policies spur growth they may at the same time lead to decreasing effectiveness of foreign aid. Second, we show that the econometric results in Burnside and Dollar e...

Let G be a finite group and let S be a G-set. The Burnside ring of G has a natural structure of a λ-ring, {λ}n∈N. However, a priori λn(S), where S is a G-set, can only be computed recursively, by first computing λ1(S), . . . , λn−1(S). In this paper we establish an explicit formula, expressing λn(S) as a linear combination of classes of G-sets.

We construct a stable homotopy refinement of quantum annular homology, link homology theory introduced by Beliakova, Putyra and Wehrli. For each $r\geq 2$ we associate to an $L$ naive $\mathbb{Z}/r\mathbb{Z}$-equivariant spectrum whose cohomology is isomorphic the as modules over $\mathbb{Z}[\mathbb{Z}/r\mathbb{Z}]$. The construction relies on equivariant version Burnside category approach Laws...