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Subgroups, Lagrange’s Theorem, Cyclic Groups

  • Cyril F. Gardiner
Part of the Universitext book series (UTX)

Abstract

Consider a group G of order p, where p is a prime integer. Suppose for the moment that our conjecture in section 2.3 that ‘the order of an element of a finite group divides the order of the group’ has been proved. There are p elements in G so there exists gG with ge. Because G is finite, g has finite order, say r > 1. Moreover by the above supposition r divides p. Now p is prime and r > 1. Hence r = p.

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Copyright information

© Springer-Verlag New York Inc. 1980

Authors and Affiliations

  • Cyril F. Gardiner
    • 1
  1. 1.Department of MathematicsUniversity of ExeterExeterEngland

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