engleski

On automorphism groups of a biplane (121,16,2)

The existence of a biplane with parameters (121, 16, 2)is an open problem. Recently, it has been proved by Alavi, Daneshkhah and Praeger that the order of an automorphism group of a possible biplane D of order 14 divides 2^7·3^2·5 ·7 ·11 ·13. In this paper we show that such a biplane does not have an automorphism of order 11 or 13, and thereby establish that |Aut(D)|divides 2^7·3^2·5 ·7. Further, we study a possible action of an automorphism group of order five or seven, and some small groups of order divisible by five or seven, on a biplane with parameters (121, 16, 2).

Symmetric design ; Biplane ; Automorphism group

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