20P05 Probabilistic methods in group theory

Overview

20P05 studies probabilistic methods in group theory in probabilistic methods in group theory. It studies random, probabilistic, and asymptotic techniques used to analyze groups and their substructures.

Related Wikipedia Page

Probabilistic Methods In Group Theory (Wikipedia)

Useful Links

• Probabilistic Methods In Group Theory (Wikipedia)
• Random group (Wikipedia)
• Probabilistic method (Wikipedia)

Key Ideas

• Canonical formulations and representative examples for probabilistic methods in group theory
• How structural, local, and computational viewpoints interact in the subject
• Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to estimate probabilities of group properties and to study random or generic group behavior.

Applications

• Random groups and subgroup growth
• Asymptotic and probabilistic group phenomena
• Randomized methods in algebra

References

• Lubotzky, A. and Segal, D. (2003) Subgroup Growth. Basel: Birkhäuser.
• Gromov, M. (1987) Hyperbolic Groups. In Essays in Group Theory, Springer LNM 8.

Recommended Textbooks

• Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill.
• Topic-focused textbook search (n.d.) Probabilistic methods in group theory. Available via Amazon search.