Mod-p group cohomology swMATH ID: 8638 Software Authors: Simon King, David Green Description: 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. Homepage: http://sage.math.washington.edu/home/SimonKing/Cohomology/ Dependencies: Sage Keywords: modular cohomology; finite groups; stable element method; projective resolution Related Software: GAP; SageMath; SINGULAR; ModIsomExt; SmallGrp; UnitLib; LAGUNA; ModIsom; LiE; Z; CHomP; QuillenSuslin; REPSN; KILLING; GCLC; SmallGroups Library; ATLAS Group Representations; MeatAxe; Cython; happrime Cited in: 9 Documents all top 5 Cited by 10 Authors 4 King, Simon A. 2 Ellis, Graham J. 2 Green, David John 1 Barthel, Tobias 1 Eick, Bettina 1 Krause, Henning 1 Margolis, Leo 1 Oehme, Markus 1 Stojanoska, Vesna 1 Symonds, Peter all top 5 Cited in 6 Serials 3 Journal of Algebra 2 Journal of Symbolic Computation 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of the American Mathematical Society 1 Algebraic & Geometric Topology 1 Oberwolfach Reports all top 5 Cited in 9 Fields 8 Group theory and generalizations (20-XX) 5 Associative rings and algebras (16-XX) 2 Commutative algebra (13-XX) 2 Category theory; homological algebra (18-XX) 2 Computer science (68-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic geometry (14-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) Citations by Year