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<p>that a<sup>2</sup> = e), then ord(a) = 2; this implies G is <a href="page.php?w=abelian_group">abelian</a> <a href="page.php?w=group_theory">since</a> . The converse is not true; for example, the (additive) <a href="page.php?w=cyclic_group">cyclic group</a> <b>Z</b><sub>6</sub> of integers <a href="page.php?w=Modular_arithmetic">modulo</a> 6 is abelian, but the number 2 has order 3:</p>

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<p>The relationship between the two concepts of order is the following: if we write<br/>
:for the <a href="page.php?w=subgroup">subgroup</a> <a href="page.php?w=Generating_set_of_a_group">generated</a></p><p>
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