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      Chapter

      The First Isomorphism Theorem
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      Chapter

      The First Isomorphism Theorem

      DOI link for The First Isomorphism Theorem

      The First Isomorphism Theorem book

      The First Isomorphism Theorem

      DOI link for The First Isomorphism Theorem

      The First Isomorphism Theorem book

      ByTony Barnard, Hugh Neill
      BookDiscovering Group Theory

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      Edition 1st Edition
      First Published 2016
      Imprint CRC Press
      Pages 6
      eBook ISBN 9781315405780
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      ABSTRACT

      Suppose that f: G → H is a homomorphism of groups and also a surjection. In Chapter 17, you saw that the kernel of a homomorphism consisted of

      those elements which map onto the identity element, and that the solution for x ∈ G of an equation such as f(x) = a is a coset in G. You find one element g ∈ G such that f(g) = a, and then you find the coset gK, where K = ker f.

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