Aufgaben:Problem 3
From Ferienserie MMP2
Revision as of 11:03, 8 June 2015 by Brynerm (Talk | contribs) (Created page with "Let G be a finite group. For a given g \in G we consider the map L_g : G \rightarrow G, g \mapsto gg'. a) Prove that L : g \mapsto L_g defines a map G \rightarrow SymG where S...")
Let G be a finite group. For a given g \in G we consider the map L_g : G \rightarrow G, g \mapsto gg'. a) Prove that L : g \mapsto L_g defines a map G \rightarrow SymG where SymG denotes the set of all invertible maps from G to G. b) Prove that the map L is injective. c) Prove that composing maps in SymG defines a group structure on SymG. d) Prove that the map L is a homomorphism of groups. e) Conclude that every finite group G can be considered a subgroup of SymG.
