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Generating set of a group

1 byte added, 04:35, 11 April 2017
* If <math>S</math> is a subset of a group <math>G</math> such that every element of <math>G</math> is a power of some element of <math>S</math>, then <math>S</math> is a generating set for <math>G</math>.
===Some examples in Abelian abelian groups===
* In the group of integers under addition, the singleton set <math>\{ 1 \}</math> is a generating set. This is because every integer can be written as a sum of <math>1</math>s or <math>-1</math>s.
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===Some examples in non-Abelian abelian groups===
* In the symmetric group on a finite set, the set of all transpositions is a generating set for the group. {{proofat|[[Transpositions generate the finitary symmetric group]]}}
[[:Category:Generating sets for particular groups]]
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