Concepedia

Concept

combinatorial group theory

Parents

564

Publications

28.6K

Citations

723

Authors

369

Institutions

About

Combinatorial group theory is a branch of mathematics that studies groups, particularly infinite groups, through the use of combinatorial techniques. It focuses on group presentations by generators and relations. This field investigates structural properties of groups by analyzing their presentations, the properties of words in the generators, and associated combinatorial objects such as Cayley graphs. Key problems addressed include algorithmic decision problems like the word problem, conjugacy problem, and isomorphism problem, as well as structural questions about subgroups and quotients. The significance lies in providing algorithmic and geometric insights into group structure and establishing fundamental connections between group theory, topology (via fundamental groups), and logic.

Top Authors

Rankings shown are based on concept H-Index.

PN

Agroscope

AM

City College of New York

GB

City College of New York

DG

Rutgers, The State University of New Jersey

DF

University of Warwick

Top Institutions

Rankings shown are based on concept H-Index.

City College of New York

New York, United States

University of Glasgow

Glasgow, United Kingdom

McGill University

Montreal, Canada

The Ohio State University

Columbus, United States