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Fundamentals of the Theory of Finite Groups

  • Guo Wenbin
Chapter
  • 252 Downloads
Part of the Mathematics and Its Applications book series (MAIA, volume 505)

Abstract

Definition 1.1.1 Let A and be two sets. If to any element a of A, a unique element b of B is assigned according to a certain rule ϕ, then ϕ is said to be a map from A to and B is written as ϕ : AB. The element b is called the image of a under ϕ and is denoted by b = ϕ(a). The element a is called an inverse image of b under ϕ. Let f be a map from A to B. If f(a) ≠ f(b) for ab, ∀a, bA, then f is said to be an injection from A to B; if for any bB, there exists an element aA such that f(a) = b, then f is said to be a surjection from A to B. If a map f is both an injection and a surjection, then f is said to be a bijection.

Keywords

Normal Subgroup Finite Group Maximal Subgroup Nilpotent Group Semidirect Product 
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 Dordrecht 2000

Authors and Affiliations

  • Guo Wenbin
    • 1
  1. 1.Mathematics DepartmentScience College, Yangzhou UniversityYangzhouP. R. China

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