Small Cancellation Theory

In the mathematical subject of group theory, small cancellation theory studies groups given by group presentations satisfying small cancellation conditions, that is where defining relations have "small overlaps" with each other. Small cancellation conditions imply algebraic, geometric and algorithmic properties of the group. Finitely presented groups satisfying sufficiently strong small cancellation conditions are word hyperbolic and have word problem solvable by Dehn's algorithm. Small cancellation methods are also used for constructing Tarski monsters, and for solutions of Burnside's problem.

Read more about Small Cancellation Theory:  History, Applications, Generalizations, Basic References

Other articles related to "small cancellation theory, small, small cancellation, theory":

Van Kampen Diagram - Generalizations and Other Applications
... Kampen diagrams are central objects in the small cancellation theory developed by Greendlinger, Lyndon and Schupp in the 1960s-1970s ... Small cancellation theory deals with group presentations where the defining relations have "small overlaps" with each other ... the geometry of reduced van Kampen diagrams over small cancellation presentations, forcing certain kinds of non-positively curved or negatively cn curved behavior ...
Small Cancellation Theory - Basic References
... Roger Lyndon and Paul Schupp, Combinatorial group theory ... Small cancellation groups ... Milé Krajčevski, Tilings of the plane, hyperbolic groups and small cancellation conditions ...

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