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- Trivial_group abstract "In mathematics, a trivial group is a group consisting of a single element. All such groups are isomorphic, so one often speaks of the trivial group. The single element of the trivial group is the identity element and so it is usually denoted as such: 0, 1 or e depending on the context. If the group operation is denoted ∗ then it is defined by e ∗ e = e.The similarly defined trivial monoid is also a group since its only element is its own inverse, and is hence the same as the trivial group.The trivial group should not be confused with the empty set (which has no elements, and lacking an identity element, cannot be a group). Given any group G, the group consisting of only the identity element is a trivial group and being a subgroup of G is called the trivial subgroup of G.The term, when referred to "G has no nontrivial proper subgroups" refers to the fact that all subgroups of G are the trivial group {e} and the group G itself.".
- Trivial_group wikiPageID "193059".
- Trivial_group wikiPageRevisionID "574718842".
- Trivial_group author "Rowland, Todd and Weisstein, Eric W.".
- Trivial_group hasPhotoCollection Trivial_group.
- Trivial_group title "Trivial Group".
- Trivial_group urlname "TrivialGroup".
- Trivial_group subject Category:Finite_groups.
- Trivial_group type Abstraction100002137.
- Trivial_group type FiniteGroups.
- Trivial_group type Group100031264.
- Trivial_group comment "In mathematics, a trivial group is a group consisting of a single element. All such groups are isomorphic, so one often speaks of the trivial group. The single element of the trivial group is the identity element and so it is usually denoted as such: 0, 1 or e depending on the context.".
- Trivial_group label "Groupe trivial".
- Trivial_group label "Grupa trywialna".
- Trivial_group label "Grupo trivial".
- Trivial_group label "Trivial group".
- Trivial_group label "Triviale Gruppe".
- Trivial_group label "Triviale groep".
- Trivial_group label "Тривиальная группа".
- Trivial_group label "當然群".
- Trivial_group sameAs Triviální_grupa.
- Trivial_group sameAs Triviale_Gruppe.
- Trivial_group sameAs Grupo_trivial.
- Trivial_group sameAs Groupe_trivial.
- Trivial_group sameAs 자명군.
- Trivial_group sameAs Triviale_groep.
- Trivial_group sameAs Grupa_trywialna.
- Trivial_group sameAs m.01bd_8.
- Trivial_group sameAs Q568687.
- Trivial_group sameAs Q568687.
- Trivial_group sameAs Trivial_group.
- Trivial_group wasDerivedFrom Trivial_group?oldid=574718842.
- Trivial_group isPrimaryTopicOf Trivial_group.