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Groups Acting on Groups

  • Hans Kurzweil
  • Bernd Stellmacher
Chapter
Part of the Universitext book series (UTX)

Abstract

The action of a group A on a set G is described by a homomorphism
$$ \pi :A \to {S_{G}} $$
; see Section 3.1. Suppose that G is not only a set but also a group. Then Aut GS G , and we say that π describes the action of A on the group G if Im π is a subgroup of Aut G. In other words, in this case the action of A on G not only satisfies O 1 and O 2 but also
$$ {\left( {gh} \right)^{a}} = {g^{a}}{h^{a}}for\;all\;g,h \in Ganda \in A $$
.

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Copyright information

© Springer-Verlag New York, Inc. 2004

Authors and Affiliations

  • Hans Kurzweil
    • 1
  • Bernd Stellmacher
    • 2
  1. 1.Institute of MathematicsUniversity of Erlangen-NuremburgErlangenGermany
  2. 2.Mathematiches Seminar KielChristian-Albrechts-UniversitätKielGermany

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