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We compare the notions of essential dimension and stable cohomologicaldimension of a finite group G, prove that the latter is bounded by the lengthof any normal series with cyclic quotients for G, and show that, however, thisbound is not sharp by showing that the stable cohomological dimension of thefinite Heisenberg groups H_p, p any prime, is equal to two.

Essential dimension, stable cohomological dimension, and stable cohomology of finite Heisenberg groups