Timeline for Algorithm for group cohomology
Current License: CC BY-SA 4.0
3 events
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| Feb 3, 2019 at 22:29 | comment | added | Derek Holt | (I am going to write $Z$ instead of ${\mathbb Z}$ for ease of typing.) Yes you define a finitely generated abelian group by its invariants, for example $[4,12,0,0]$ for $Z/(4Z) \oplus Z/(12Z) \oplus Z^2$, and then you define the action of the group $G$ on this group by matrices defining the action of the group generators. In this example they would be $4 \times 4$ matrices over $Z$. In the example I gave the modules were ${\mathbb F}_2G$-modules. | |
| Feb 3, 2019 at 21:40 | comment | added | S. du Val | By abelian invariants you mean the structure as finitely generated abelian groups? In my case, $M_2$ and $M_3$ are most naturally expressed as quotients of a (common) lattice by suitable sublattices (actually $M_3$ is also a lattice, but $M_2$ is not). Also, it seems to me that $N$ and $M$ are modules over $\mathbb{F}_2$ instead of $G$, am I wrong? Are there difficulties to consider $\mathbb Z$-modules in magma? | |
| Feb 3, 2019 at 21:09 | history | answered | Derek Holt | CC BY-SA 4.0 |