On the cup product for groups

Dyer, M. N.; Leahy, J. V.; Mooney, L. J.

doi:10.1090/S0002-9939-1992-1093596-6

On the cup product for groups
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by M. N. Dyer, J. V. Leahy and L. J. Mooney

Proc. Amer. Math. Soc. 116 (1992), 219-227

DOI: https://doi.org/10.1090/S0002-9939-1992-1093596-6

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Abstract:

For $G$ any group and trivial coefficients in $R$, a commutative ring, the authors analyze the kernel of the cup product $\cup :{H^1}\left ( {G,R} \right ) \otimes {H^1}\left ( {G,R} \right ) \to {H^2}\left ( {G,R} \right )$ by splicing it together with part of the six-term Hom-Ext exact sequence obtained from $0 \to {I^2}/{I^3} \to I/{I^3} \to I/{I^2} \to 0$.

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