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PDF-De nition-Lemma23.3.SupposethegroupGactsonthesetS.Givens2SthesubsetH=f

PDF-De nition-Lemma23.3.SupposethegroupGactsonthesetS.Givens2SthesubsetH=f

Author : sherrill-nordquist | Published Date : 2016-05-12

jHjProofDe neamapfLSbysendingtheleftcosetgHtotheelementgsWe rsthavetocheckthatfiswellde nedSupposethatgHg0HTheng0ghforsomeh2HButtheng0sghsghsgsThusfisindeedwellde nedfiscl

jHj:Proof.De neamapf:L!SbysendingtheleftcosetgHtotheelementgs.We rsthavetocheckthatfiswell-de ned.SupposethatgH=g0H.Theng0=gh forsomeh2H.Buttheng0s=(gh)s=g(hs)=gs:Thusfisindeedwell-de ned.fiscl

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De nition-Lemma23.3.SupposethegroupGactsonthesetS.Givens2SthesubsetH=f: Transcript

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