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Let $G=H\times J$, where $H\cong J\cong C_2$ (cyclic group of order 2). Let $M \cong \mathbb{Z}$ be a $G$-module via "trivial $H$-action and negation $J$-action". My question is "What are the group ...

The following sentence is quoted from the paper ON THE COHOMOLOGY OF SPLIT EXTENSIONS by D. J. BENSON AND M. FESHBACH: In general, the differentials in the Lyndon-Hochschild-Serre spectral sequence ...