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A monoid in which every element has an inverse.
wp-groupnlab-groupstacks-algebra-textEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Based loops modulo homotopy form a group under concatenation.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
hatcher-algebraic-topologywp-groupnlab-groupThis is an authored directed relation from the source endpoint to the target endpoint.
Require every element to have a two-sided inverse.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-groupnlab-groupstacks-algebra-textThis is an authored directed relation from the source endpoint to the target endpoint.
Forgetting the terminating derived or subnormal series leaves the underlying group.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
milne-fields-galois-theoryEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require .
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-abelianstacks-algebra-textThis is an authored directed relation from the source endpoint to the target endpoint.
A Galois group is a group, with composition as operation.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
milne-fields-galois-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
A group is precisely a groupoid with one object: group elements are the invertible endomorphisms.
Reinterpret an object, pass to an equivalent presentation, or relate canonically corresponding structures; the carrier may change.
wp-groupwp-groupoidriehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
Supply the Group structure as one jointly required input.
Feed several structures into a construction junction and impose compatibility between them.
wp-group-actionnlab-group-actionetingof-representation-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Supply the Group structure as one jointly required input.
Feed several structures into a construction junction and impose compatibility between them.
wp-group-representationnlab-representationetingof-representation-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Supply the Group structure as one jointly required input.
Feed several structures into a construction junction and impose compatibility between them.
wp-lattice-ordered-groupgierz-orderThis is an authored directed relation from the source endpoint to the target endpoint.
Supply the group structure on the same carrier as the smooth manifold.
Feed several structures into a construction junction and impose compatibility between them.
nlab-lie-groupwp-grouplee-smooth-manifoldsThis is an authored directed relation from the source endpoint to the target endpoint.
Use the group operations on the common carrier.
Feed several structures into a construction junction and impose compatibility between them.
wp-ordered-groupgierz-orderThis is an authored directed relation from the source endpoint to the target endpoint.
Supply the group operations.
Feed several structures into a construction junction and impose compatibility between them.
wp-top-grouptopology-without-tears