Detecting ends of residually finite groups in profinite completions

Let \C be a variety of finite groups. We use profinite Bass--Serre theory to show that if $u:H\hookrightarrow G$ is a map of finitely generated residually \C groups such that the induced map $\hat{u}:\hat{H}\rightarrow\hat{G}$ is a surjection of the pro-\C completions, and $G$ has more than one end, then $H$ has the same number of ends as $G$. However if $G$ has one end the number of ends of $H$ may be larger; we observe cases where this occurs for \C the class of finite $p$-groups. We produce a monomorphism of groups $u:H\hookrightarrow G$ such that: either $G$ is hyperbolic but not residually finite; or $\hat{u}:\hat{H}\rightarrow\hat{G}$ is an isomorphism of profinite completions but $H$ has property (T) (and hence (FA)), but $G$ has neither. Either possibility would give new examples of pathological finitely generated groups

Distinguishing geometries using finite quotients

We prove that the profinite completion of the fundamental group of a compact 3-manifold M satisfies a Tits alternative: if a closed subgroup H does not contain a free pro-p subgroup for any p, then H is virtually soluble, and furthermore of a very particular form. In particular, the profinite completion of the fundamental group of a closed, hyperbolic 3-manifold does not contain a subgroup isomorphic to Zb2. This gives a profinite characterization of hyperbolicity among irreducible 3-manifolds. We also characterize Seifert fibred 3-manifolds as precisely those for which the profinite completion of the fundamental group has a non-trivial procyclic normal subgroup. Our techniques also apply to hyperbolic, virtually special groups, in the sense of Haglund and Wise. Finally, we prove that every finitely generated pro-p subgroup of the profinite completion of a torsion-free, hyperbolic, virtually special group is free pro-p.Wilton is supported by the EPSRC and Zalesskii by CNPq and CAPES

Prime ideals in nilpotent Iwasawa algebras

Let G be a nilpotent complete p-valued group of finite rank and let k be a field of characteristic p. We prove that every faithful prime ideal of the Iwasawa algebra kG is controlled by the centre of G, and use this to show that the prime spectrum of kG is a disjoint union of commutative strata. We also show that every prime ideal of kG is completely prime. The key ingredient in the proof is the construction of a non-commutative valuation on certain filtered simple Artinian rings

Dielectric properties of PbBO₃ perovskites with mixed-valence substitution in the B position

Dielectric properties of PbBO₃ perovskites with mixed-valence substitution in the B position / V. G. Zalesskiĭ, V. V. LemanovThis paper reports on the synthesis of PbBO3 perovskites with mixed-valence substitution in the B position in which the number of ions n in different valence states occupying oxygen octahedra varies from 2 to 6. The dielectric properties of ceramic samples have been studied at frequencies in the range from 12 Hz to 100 kHz and in the temperature interval 77–450 K. The new compounds have been shown to possess relaxor properties. Original Russian Text © V.G. Zalesskiĭ, V.V. Lemanov, 2010, published in Fizika Tverdogo Tela, 2010, Vol. 52, No. 7, pp. 1365–1369

Materialy k poznaniiu iskopaemoi flory Dombrovskago kamennougol'nago basseina. : Beiträge zur kenntnis der fossilen flora des steinkohlenreviers von Dombrowa /

Text in Russian and German.Bibliographical foot-notes.Mode of access: Internet