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In group theory, a branch of mathematics, an opposite group is a way to construct a group from another group that allows one to define right action as a special case of left action.
Monoids, groups, rings, and algebras can be viewed as categories with a single object. The construction of the opposite category generalizes the opposite group, opposite ring, etc.
Definition
[edit]Let be a group under the operation . The opposite group of , denoted , has the same underlying set as , and its group operation is defined by .
If is abelian, then it is equal to its opposite group. Also, every group (not necessarily abelian) is naturally isomorphic to its opposite group: An isomorphism is given by . More generally, any antiautomorphism gives rise to a corresponding isomorphism via , since
Group action
[edit]Let be an object in some category, and be a right action. Then is a left action defined by , or .
Well, that’s interesting to know that Psilotum nudum are known as whisk ferns. Psilotum nudum is the commoner species of the two. While the P. flaccidum is a rare species and is found in the tropical islands. Both the species are usually epiphytic in habit and grow upon tree ferns. These species may also be terrestrial and grow in humus or in the crevices of the rocks.
View the detailed Guide of Psilotum nudum: Detailed Study Of Psilotum Nudum (Whisk Fern), Classification, Anatomy, Reproduction