Difference between revisions of "Trivial subgroup"

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==Definition==
 
==Definition==
  
The ''trivial property'' is the [[subgroup property]] of being the trivial subgroup. In other words, a subgroup of a group is said to satisfy the ''trivial property'' if and only if it is the trivial subgroup (the subgroup comprising only the identity element).
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A subgroup of a group is said to be the '''trivial subgroup''' or satisfy the ''trivial property'' if and only if it is the [[trivial group]] (viz the group with one element, the identity element).
  
 
==Relation with other properties==
 
==Relation with other properties==

Latest revision as of 00:33, 8 May 2008

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

A subgroup of a group is said to be the trivial subgroup or satisfy the trivial property if and only if it is the trivial group (viz the group with one element, the identity element).

Relation with other properties

Related metaproperties