{"type":"standard","title":"Cauchy's theorem (group theory)","displaytitle":"Cauchy's theorem (group theory)","namespace":{"id":0,"text":""},"wikibase_item":"Q1139041","titles":{"canonical":"Cauchy's_theorem_(group_theory)","normalized":"Cauchy's theorem (group theory)","display":"Cauchy's theorem (group theory)"},"pageid":2838129,"thumbnail":{"source":"https://upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Cyclic_group.svg/330px-Cyclic_group.svg.png","width":320,"height":311},"originalimage":{"source":"https://upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Cyclic_group.svg/443px-Cyclic_group.svg.png","width":443,"height":431},"lang":"en","dir":"ltr","revision":"1255382677","tid":"a68f79dc-9ad2-11ef-b4e9-1a1e04cb3212","timestamp":"2024-11-04T17:31:40Z","description":"Existence of group elements of prime order","description_source":"local","content_urls":{"desktop":{"page":"https://en.wikipedia.org/wiki/Cauchy's_theorem_(group_theory)","revisions":"https://en.wikipedia.org/wiki/Cauchy's_theorem_(group_theory)?action=history","edit":"https://en.wikipedia.org/wiki/Cauchy's_theorem_(group_theory)?action=edit","talk":"https://en.wikipedia.org/wiki/Talk:Cauchy's_theorem_(group_theory)"},"mobile":{"page":"https://en.m.wikipedia.org/wiki/Cauchy's_theorem_(group_theory)","revisions":"https://en.m.wikipedia.org/wiki/Special:History/Cauchy's_theorem_(group_theory)","edit":"https://en.m.wikipedia.org/wiki/Cauchy's_theorem_(group_theory)?action=edit","talk":"https://en.m.wikipedia.org/wiki/Talk:Cauchy's_theorem_(group_theory)"}},"extract":"In mathematics, specifically group theory, Cauchy's theorem states that if G is a finite group and p is a prime number dividing the order of G, then G contains an element of order p. That is, there is x in G such that p is the smallest positive integer with xp = e, where e is the identity element of G. It is named after Augustin-Louis Cauchy, who discovered it in 1845.","extract_html":"
In mathematics, specifically group theory, Cauchy's theorem states that if G is a finite group and p is a prime number dividing the order of G, then G contains an element of order p. That is, there is x in G such that p is the smallest positive integer with xp = e, where e is the identity element of G. It is named after Augustin-Louis Cauchy, who discovered it in 1845.
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{"fact":"All cats have three sets of long hairs that are sensitive to pressure - whiskers, eyebrows,and the hairs between their paw pads.","length":128}
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