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Extremely primitive groups and linear spaces

Haiyan Guan, Shenglin Zhou (2016)

Czechoslovak Mathematical Journal

A non-regular primitive permutation group is called extremely primitive if a point stabilizer acts primitively on each of its nontrivial orbits. Let 𝒮 be a nontrivial finite regular linear space and G Aut ( 𝒮 ) . Suppose that G is extremely primitive on points and let rank ( G ) be the rank of G on points. We prove that rank ( G ) 4 with few exceptions. Moreover, we show that Soc ( G ) is neither a sporadic group nor an alternating group, and G = PSL ( 2 , q ) with q + 1 a Fermat prime if Soc ( G ) is a finite classical simple group.

Generalizations of Cole's Systems

Gizatullin, Marat (1996)

Serdica Mathematical Journal

There are four resolvable Steiner triple systems on fifteen elements. Some generalizations of these systems are presented here.

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