Infinite cyclic projective skew translation quadrangles do not exist
Koen Thas
TL;DR
This paper proves that infinite cyclic projective skew translation quadrangles do not exist, completing their classification and revealing they only occur in finite cases.
Contribution
The paper introduces a new approach to classify infinite cyclic projective skew translation quadrangles and demonstrates their non-existence in the infinite case.
Findings
Infinite cyclic projective skew translation quadrangles do not exist.
The classification method is adapted from finite to infinite cases.
Only finite cyclic projective skew translation quadrangles exist.
Abstract
In this paper we completely classify infinite cyclic projective skew translation quadrangles through a new approach first partially introduced in [17], and in the present paper (unexpectedly) adapted to the infinite case. Very surprisingly, these objects do not exist and only occur in the finite case.
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Taxonomy
TopicsFinite Group Theory Research · graph theory and CDMA systems · Coding theory and cryptography