##  [Inflation–Restriction Exact Sequence](/inflation-restriction-exact-sequence) 

  ##  [Inflation–Restriction Exact Sequence](https://puremath.quantumdictionary.io/inflation-restriction-exact-sequence-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A low-degree exact sequence in group cohomology relating the cohomology of a group G, a normal subgroup N, and the quotient Q = G/N via the inflation and restriction maps; it is obtained as the edge sequence of the Hochschild–Serre spectral sequence and supplies exact relations among H^i(Q, M^N), H^i(G,M) and H^i(N,M)^{Q} in small degrees.