On group-theoretic models of randomness and genericity
Ilya Kapovich, Paul Schupp
TL;DR
This paper compares two models of randomness in group theory: Gromov's random group model and the generic groups model of Arzhantseva and Ol'shanskii, analyzing their similarities and differences.
Contribution
It provides a detailed comparison of two prominent models of randomness in group theory, highlighting their conceptual and technical distinctions.
Findings
Identifies key differences between the models
Analyzes the implications for group properties
Provides insights into the nature of genericity in groups
Abstract
We compare the random group model of Gromov and the model of generic groups of Arzhantseva and Ol'shanskii.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Operator Algebra Research · Mathematical Dynamics and Fractals