Using Cayley's theorem to find the order of a power in a group

• Autores: David E. Dobbs
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 44, Nº. 3, 2013, págs. 417-423
• Idioma: inglés
• DOI: 10.1080/0020739x.2012.703340
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• Resumen

  • It is shown how Cayley's theorem can be used to prove the formula for the order of a power of an element of finite order in a group. Reasoning with disjoint cycles leads to a proof that depends on elementary number theory in some new ways, leading naturally to some new connections involving least common multiples, greatest common divisors and minima.