A biplane is a (v, k, 2) design, that is, a structure of v points and v blocks such that every point belongs to exactly k blocks, and every pair of blocks is incident with exactly two points. The only values of k for which examples of biplanes are known are k=3, 4, 5, 6, 9, 11, and 13.

To find other examples of biplanes, many techniques can be used, such as construction methods and computer searches. An alternative method is to assume that there is a particular group of permutations leaving the biplane invariant, and to classify the biplanes as invariant under this particular group of permutations. Either the classification shows that the known examples invariant under this group are effectively the only examples invariant under this group, or new examples arise during the classification, which is what one hopes for.

This work continues similar work in this field. In another paper by the same author [1], the biplanes admitting an imprimitive flag-transitive group are classified, and it is proved that if a biplane admits a primitive flag-transitive group, then the group is of affine or almost simple type in the O’Nan-Scott classification. The affine case was analyzed by the author [1]. Now, she shows that there are no biplanes admitting a primitive flag-transitive automorphism group of almost simple type, with alternating or sporadic socle.