A lattice $(X,\le)$ is twisted self-dual iff it is self-dual but there is not any self-duality $f:X\to X$ with $f\circ f=1_X$.
Is there any group with lattice of all its subgroups twisted self-dual?
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$\begingroup$ The work of Pogel is related. $\endgroup$– TriJan 8, 2016 at 18:48
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