Mod-p group cohomology
This is an optional package for the Sage computer algebra system. It computes modular cohomology rings of finite groups. It yields minimal presentations of the cohomology rings, can compute various ring invariants (Poincaré series, a-invariant, depth, ...) and also the nil-radical and essential classes. It provided the first complete computation of the mod-2 cohomology rings of all groups of order 128. It was also used to compute the mod-p cohomology of various finite simple groups (for different primes p), including the first computation of the mod-2 cohomology ring of the third Conway group, showing that this ring is Cohen-Macaulay.
Keywords for this software
References in zbMATH (referenced in 7 articles )
Showing results 1 to 7 of 7.
- Eick, Bettina; King, Simon: The isomorphism problem for graded algebras and its application to $\mathrmmod-p$ cohomology rings of small $p$-groups. (2016)
- Oehme, Markus: The mod-2 cohomology of $32\Gamma_3f$. (2016)
- King, Simon A.: A non-commutative $F_5$ algorithm with an application to the computation of Loewy layers. (2014)
- Ellis, Graham; Smith, Paul: Computing group cohomology rings from the Lyndon-Hochschild-Serre spectral sequence. (2011)
- Green, David J.; King, Simon A.: The computation of the cohomology rings of all groups of order 128. (2011)
- King, Simon A.; Green, David J.; Ellis, Graham: The mod-2 cohomology ring of the third Conway group is Cohen-Macaulay. (2011)
- Symonds, Peter: On the Castelnuovo-Mumford regularity of the cohomology ring of a group. (2010)