Two questions of Moorhouse on indiscernible locally finite generalized quadrangles

TL;DR

This paper resolves two open questions about the existence of certain locally finite generalized quadrangles with specific indiscernible structures, advancing understanding in finite geometry.

Contribution

It provides definitive answers to Moorhouse's questions regarding the existence of indiscernible ovoids or spreads in locally finite generalized quadrangles.

Findings

Confirmed the existence/non-existence of indiscernible ovoids.

Confirmed the existence/non-existence of indiscernible spreads.

Clarified conditions under which such structures can or cannot exist.

Abstract

We settle two questions posed by G. Eric Moorhouse on the existence of locally finite generalized quadrangles with indiscernible ovoids or spreads.