##  [Shapiro's Lemma](/shapiros-lemma) 

  ##  [Shapiro's Lemma](https://puremath.quantumdictionary.io/shapiros-lemma-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An isomorphism in group cohomology that identifies the cohomology of an induced module with the cohomology over the inducing subgroup: for a subgroup H ≤ G and an H-module M, H^n(G, Ind_H^G M) ≅ H^n(H, M) for all n (with the appropriate hypotheses on modules and topology).