Essential dimension, stable cohomological dimension, and stable cohomology of finite Heisenberg groups
Abstract
We compare the notions of essential dimension and stable cohomological dimension of a finite group G, prove that the latter is bounded by the length of any normal series with cyclic quotients for G, and show that, however, this bound is not sharp by showing that the stable cohomological dimension of the finite Heisenberg groups Hp, p any prime, is equal to two.
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