Partial Linear Spaces With Dual Affine Planes

Orbits of Groups Generated by Transvections over F2

“…The one-element B R -orbits in F B R 2 are 0, b 2 + b 4 + b 5 , b 2 + b 4 + b 1 , b 1 + b 5 and the remaining one is represented by b 1 , so there is a total of 10 B -orbits in v + F B R 2 for any v ∈ {0, v 3 + v 1 + b 6 }. According to Theorem 2.16, the remaining orbits are represented by the vectors v 3 , v 3 …”

“…On the other hand, Hall obtained a classification of a class of 3-transposition groups which include certain groups generated by symplectic transvections [10,11]. Furthermore, Hall extended Shult's classification of certain partial linear spaces in polar geometry [3,10,11]. Hall also gave some group theoretical properties of symplectic transvections and discussed applications to the topology of surfaces and mapping class groups [9].…”