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A (0,  α )-geometry,  α  ≥ 3, fully embedded in AG( n ,  q ) is always a linear representation[2]. In [4] the (0, 2)-geometries fully embedded in AG(3,  q ) are classied up to linear representations. Here we extend this result to full embeddings in AG( n ,  q ). As a corollary we classify the semipartial geometries with  α  &gt; 1 fully embedded in AG( n ,  q ), but not as a linear representation.

The embedding of (0, 2)-geometries and semipartial geometries in AG( n, q )