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In mathematics, the 'trivial group' is the group consisting of a single element, variously labeled ''e'', ''1'', or ''0''. The group operation is ''e'' + ''e'' = ''e''. The identity element is, of course, ''e'', and the group is abelian; all these results being trivial, hence the name. The trivial group is often written as 'Z'1 or just 0 or ''e''.
The trivial group should not be confused with the empty set (which has no elements and therefore, lacking an identity element, cannot be a group), though both play similar roles in their respective categories.
Every group contains a trivial subgroup.
★ List of small groups
The trivial group should not be confused with the empty set (which has no elements and therefore, lacking an identity element, cannot be a group), though both play similar roles in their respective categories.
Every group contains a trivial subgroup.
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| See also |
See also
★ List of small groups
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