# Changes

## Group cohomology of elementary abelian group of prime-square order

, 21:12, 24 October 2011
Important case types for abelian groups
| [itex]M[/itex] is uniquely [itex]p[/itex]-divisible, i.e., every element of [itex]M[/itex] can be divided by <matH>p[/itex] uniquely. This includes the case that [itex]M[/itex] is a field of characteristic not 2. || all zero groups || all zero groups
|-
| [itex]M[/itex] is [itex]p[/itex]-torsion-free, i.e., no nonzero element of [itex]M[/itex] multiplies by [itex]p[/itex] to give zero. || [itex](M/pM)^{(q-31)/2}[/itex] || [itex](M/pM)^{(q+2)/2}[/itex]
|-
| [itex]M[/itex] is [itex]p[/itex]-divisible, but not necessarily uniquely so, e.g., [itex]M = \mathbb{Q}/\mathbb{Z}[/itex] || [itex](\operatorname{Ann}_M(p))^{(q+3)/2}[/itex] || [itex](\operatorname{Ann}_M(p))^{q/2}[/itex]