Abstract
We will give an efficient bimodule projective resolution of an order Γ, where Γ is an order of a simple component of the rational group ring ℚ Q 2 r of the generalized quaternion 2-group Q 2 r of order 2 r+2. Moreover, we will determine the ring structure of the Hochschild cohomology HH*(Γ) by calculating the Yoneda products using this bimodule projective resolution.
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