Elementary Properties of Symplectic Amalgams

Abstract

For the remainder of this monograph (with the exception of Chapter 24) A(P ₁, P ₂, P ₁₂) denotes a symplectic amalgam over GF(q), q = p ^a, p a prime. Also G will always denote the universal completion of this amalgam (so G = P ₁*p ₁₂ P ₂). We recall that P ₁, P ₂ and P ₁₂ may be identified as subgroups of G with P ₁ ∩ P ₂ = P ₁₂. Note that P ₁ and P₂ sire different subgroups of G and that G = ‹P ₁,P ₂›