Group exponent

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In the mathematical sub-area of group theory , the group exponent of a group is understood to be the smallest natural number for which ( power of a group element ) applies to all group elements . If there is no such number, it is said that it has an exponent (it must then also be of infinite order ).



  • For the prime residual class groups , the group exponent is obtained from the Carmichael function .
  • The group exponent of with a prime number is equal to the group order .
  • The group exponent of is 2 (compare: The group order is 4).
  • The body with elements, understood as an additive group, has group order and group exponent (compare characteristics of a body ).
  • Infinite groups with finite exponents are, for example, the polynomial ring and the algebraic closure of , each (because of the prime number characteristic ) in the additive combination.
  • Every element of the (infinite) torsion group has finite order if it holds and is too coprime . Since the element orders are not restricted, is .

See also

Individual evidence

  1. ^ Wikiversity. Retrieved August 13, 2012.
  2. Matroids Math Planet. Post No. 7 from Gockel. Retrieved August 13, 2012.