On periodic groups with prescribed orders of elements

This is a survey of results and open problems concerning the structure of periodic group with prescribed orders of their elements. In particular, an outline of a proof of the following recent result is given: every periodic group whose set of element orders coincides with {1,2,3,4,8} is locally finite.     

Thompson’s conjecture for Lie type groups E 7(q)

In this article, we prove a conjecture of Thompson for an infinite class of simple groups of Lie type E ₇(q). More precisely, we show that every finite group G with the properties Z(G) = 1 and cs(G) = cs(E ₇(q)) is necessarily isomorphic to E ₇(q), where cs(G) and Z(G) are the set of lengths of conjugacy classes of G and the center of G respectively.     

Chemoselective immobilization of biomolecules through aqueous Diels-Alder and PEG chemistry

Aqueous Diels-Alder chemistry combined with a poly(ethylene glycol) (PEG) spacer was used to immobilize a diverse group of biomolecules onto a solid surface. Briefly, α, ω linear PEG conjugates were synthesized containing cyclopentadiene in the α position and either biotin, lactose, or protein A in the ω position. Linkers were coupled to N-maleimide (EMC)-functionalized glass substrates, and surface immobilization of biomolecules was confirmed by confocal fluorescence imaging.     

关于Thompson问题

1987年本文第二作者给J.G.Thompson教授的信中提出猜想:所有有限单群S,都能够用S的阶和S的元的阶的集合统一的刻画.在回信中,Thompson提出了他的关于有限群G可解性判断的问题.当G的素图非连通时,本文给出了J.G.Thompson问题的肯定回答.