Abstract
The action of a group A on a set G is described by a homomorphism
; see Section 3.1. Suppose that G is not only a set but also a group. Then Aut G ≤ S 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
.
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© 2004 Springer-Verlag New York, Inc.
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Kurzweil, H., Stellmacher, B. (2004). Groups Acting on Groups. In: The Theory of Finite Groups. Universitext. Springer, New York, NY. https://doi.org/10.1007/0-387-21768-1_8
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DOI: https://doi.org/10.1007/0-387-21768-1_8
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