Difference between revisions of "Aufgaben:Problem 3"

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Let G be a finite group. For a given g \in G we consider the map L_g : G \rightarrow G, g \mapsto gg'.
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a) Prove that L : g \mapsto L_g defines a map G \rightarrow SymG where SymG denotes the set of
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all invertible maps from G to G.
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b) Prove that the map L is injective.
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c) Prove that composing maps in SymG defines a group structure on SymG.
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d) Prove that the map L is a homomorphism of groups.
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e) Conclude that every finite group G can be considered a subgroup of SymG.
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Revision as of 11:08, 8 June 2015

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