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On Groups

  • Lindsay N. Childs
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

In Section 9E we proved the abstract Fermat theorem: if G is an abelian group with n elements, then a n = e for any a in G. In this section we will show that if H is any subgroup of G, then the number of elements of H is a divisor of the number of elements of G. This famous result is called Lagrange’s theorem. Euler’s and Fermat’s theorems are easy consequences of Lagrange’s theorem.

Keywords

Finite Group Identity Element Group Homomorphism Rigid Motion Ring Homomorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Lindsay N. Childs
    • 1
  1. 1.Department of MathematicsSUNY at AlbanyAlbanyUSA

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