Abstract
Let G be a finite group, V a faithful finite-dimensional representation of G over the complex field and be the corresponding invariant field. The Bogomolov multiplier of G is canonically isomorphic to the unramified cohomological group which has been used by Saltman in 1984 and Bogomolov in 1988 to provide counterexamples to the rationality problem of for finite p-groups P over In this paper, we investigate the vanishing property of where P denotes a p-group of order p 6 for
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