The Schur Multiplier, Profinite Completions and Decidability

Decidability and Tameness in the Theory of Finite Semigroups

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...

Characterization of finite $p$-groups by the order of their Schur multipliers ($t(G)=7$)

‎Let $G$ be a finite $p$-group of order $p^n$ and‎ ‎$|{mathcal M}(G)|=p^{frac{1}{2}n(n-1)-t(G)}$‎, ‎where ${mathcal M}(G)$‎ ‎is the Schur multiplier of $G$ and $t(G)$ is a nonnegative integer‎. ‎The classification of such groups $G$ is already known for $t(G)leq‎ ‎6$‎. ‎This paper extends the classification to $t(G)=7$.

Profinite completions of some groups acting on trees

We investigate the profinite completions of a certain family of groups acting on trees. It turns out that for some of the groups considered, the completions coincide with the closures of the groups in the full group of tree automorphisms. However, we introduce an infinite series of groups for which that is not so, and describe the kernels of natural homomorphisms of the profinite completions on...

On the Phan system of the Schur cover of SU(4, 32)

This article is part of the program described in [3]. We study the Phan amalgams and their universal completions that occur for q = 3 in rank n = 3 for the diagram A3 = D3, corresponding to SU(4, 3) ∼= Spin−(6, 3). We show that the associated geometries admit universal 9-fold coverings, by showing that the universal completion of the Phan amalgam is the central extension of SU(4, 3) by its Schu...