Infinite groups : geometric, combinatorial and dynamical aspects

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Structure and finiteness properties of subdirect products of groups (2007, background): “Work by various authors has exposed the surprisingly rich structure to be found amongst the subdirect products of superficially tame groups.”
Evaluations of Noncommutative Polynomials on Algebras: Methods and Problems, and the L'vov-Kaplansky Conjecture (2020, background): “Investigation of the image sets of words in pro-p-groups is related to the investigation of Lie polynomials and helped Zelmanov [108] to prove that the free pro-p-group cannot be embedded in the algebra of n× n matrices when p n.”
Subgroups of direct products of limit groups (2007, background): “For simplicity of exposition, the homology of a group G in this paper will almost always be with coefficients in a Q G-module – typically the trivial module Q.”
On the finite presentation of subdirect products and the nature of residually free groups (2012, methodology): “The proof of Theorem D relies on our earlier work concerning the finiteness properties of subgroups of direct products of limit groups [12] as well as Theorem A (the VSP criterion).”
REPRESENTABILITY AND SPECHT PROBLEM FOR G-GRADED ALGEBRAS (2009, background): “Then there exists a field extension K of F and a finite dimensional algebra A over K such that idG(W ) = idG(A).”