Editing Geometric Group Theory (section)

== <span style="color: #FFFFFF;">Remembering</span> ==
* '''Geometric Group Theory (GGT)''' — Studying groups through their actions on geometric spaces.
* '''Group''' — A set of elements with an operation (like addition) that follows specific rules.
* '''Cayley Graph''' — A visual "map" of a group where elements are points and operations are connecting lines.
* '''Hyperbolic Group''' — A group whose Cayley graph "looks like" hyperbolic (curved) space.
* '''Word Metric''' — Measuring the distance between two elements by the number of steps needed to get from one to the other.
* '''Quasi-Isometry''' — A way of saying two shapes look the same from "far away," even if they are different up close.
* '''Action''' — When a group "moves" or "transforms" a space (e.g., rotating a square).
* '''Mikhail Gromov''' — The founder of modern GGT who introduced the idea of "Hyperbolic Groups."
* '''Free Group''' — A group with no "loops"—its map looks like a tree that branches infinitely.
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