Z8 is not dualizable
Abstract
In this paper we show that Z8 does not admit a natural duality. In fact, we show that 2Z8 = 2, 4, 6, 8 | +,. is not dualizable, and this will imply that the original ring is not dualizable, either. As a corollary we show that Sindi's conjecture does not hold. Our technique will be similar to one due to Quackenbush and Szab\'o, where non-dualizability is proved for the quaternion group.
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