https://tcs.nju.edu.cn/wiki/api.php?action=feedcontributions&feedformat=atom&user=173.73.183.30TCS Wiki - User contributions [en]2026-05-26T19:06:33ZUser contributionsMediaWiki 1.45.3https://tcs.nju.edu.cn/wiki/index.php?title=Lagrange%27s_theorem_(group_theory)&diff=7699Lagrange's theorem (group theory)2017-03-20T01:27:33Z<p>173.73.183.30: Added some applications, and explained what |H| meant.</p>
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'''Lagrange's theorem''' in [[group theory]] states if G is a finite [[group (mathematics)|group]] and H is a [[subgroup]] of G, then |H| (how many elements are in H, called the order of H) divides |G|. Moreover, the number of distinct left (right) [[coset]]s of H in G is |G|/|H|. <br />
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'''Applications''' <br />
* For any g in a group G, <math>g^k=e</math> for some k that divides the |G| <br />
* Any group of prime order cyclic (Any element in G can be created by a single element) and simple (no normal subgroups that aren't trivial) <br />
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[[Category:Algebra]]</div>173.73.183.30