arXiv subjects
Publications and source records attributed to Stephen Majewicz.
In this paper we compute the Chermak-Delgado measure of the mod $p^{n}$ Heisenberg Group for any prime $p$. To achieve this we introduce the notion of the pseudocentralizer and prove various results about it.
In this paper, we study nilpotent $\mathbb{Q}$$[x]$-powered groups that satisfy the following property: For some set of primes $ω$ in $\mathbb{Q}$$[x]$, every $ω'$-isolated $\mathbb{Q}$$[x]$-subgroup in some family of its $\mathbb{Q}$$[x]$-subgroups is finite $ω$-type separable.
In this paper we study conjugacy and subgroup separability properties in the class of nilpotent $\mathbb{Q}[x]$-powered groups. Many of the techniques used to study these properties in the context of ordinary nilpotent groups carry over naturally to this more general class. Among other results, we offer a generalization of a theorem due to G. Baumslag. The generalized version states that if $G$ is a finitely $\mathbb{Q}[x]$-generated $\mathbb{Q}[x]$-torsion-free nilpotent $\mathbb{Q}[x]$-powered group and $H$ is a $\mathbb{Q}[x]$-isolated subgroup of $G,$ then for any prime $π\in \mathbb{Q}[x]$, $\bigcap_{i = 1}^{\infty} G^{π^{i}}H = H.$
In this paper, we study the residual solvability of the generalized free product of solvable groups.