A group may be considered C⁎-stable if almost representations of the group in a C⁎-
algebra are always close to actual representations. We initiate a systematic study of which …

In this paper, we introduce two general schemes of algebraic cryptography. We show that
many of the systems and protocols considered in literature that use two-sided multiplications …

The goalofthisbookis toshowcasenewdirectionsingroup theorymotivated bycomputer
science. The subtitle (GAGTA book) reflects the fact that the book follows the courseoftheGeometricandAsymptoticGroup …

In this paper we show that the Diophantine problem in solvable Baumslag–Solitar groups $
BS (1, k) $ and in wreath products $ A\wr\mathbb {Z} $, where $ A $ is a finitely generated …

We solve the following algorithmic problems using TC 0 circuits, or in logspace and
quasilinear time, uniformly in the class of nilpotent groups with bounded nilpotency class …

Abstract Post's Correspondence Problem (the PCP) is a classical decision problem in
theoretical computer science that asks whether for pairs of free monoid morphisms g, h …

We consider two fields of study–random groups and cubulations–from their definitions and
history to current research. Motivated by group properties, we apply cubulation theory to a …

In this short survey we describe recent advances on the Post Correspondence Problem in
group theory that were inspired by results in computer science. These algebraic advances …

We study finitely generated nilpotent groups G given by full rank finite presentations< A| R>
N c in the variety N c of nilpotent groups of class at most c, where c≥ 2. We prove that if the …

We study metabelian groups 𝐺 given by full rank finite presentations⟨ A∣ R⟩ M in the
variety ℳ of metabelian groups. We prove that 𝐺 is a product of a free metabelian subgroup …