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Point regular groups of automorphisms of generalised quadrangles
Combinatorics · Submitted 13 May 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In particular we determine all point regular groups of automorphisms of the thick classical generalised quadrangles.
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The abstract, sentence by sentence
We study the point regular groups of automorphisms of some of the known generalised quadrangles. In particular we determine all point regular groups of automorphisms of the thick classical generalised quadrangles. We also construct point regular groups of automorphisms of the generalised quadrangle of order $(q-1,q+1)$ obtained by Payne derivation from the classical symplectic quadrangle $\mathsf{W}(3,q)$. For $q=p^f$ with $f\geq 2$ we obtain at least two nonisomorphic groups when $p\geq 5$ and at least three nonisomorphic groups when $p=2$ or $3$. Our groups include nonabelian 2-groups, groups of exponent 9 and nonspecial $p$-groups. We also enumerate all point regular groups of automorphisms of some small generalised quadrangles.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the point regular groups of automorphisms of some of the known generalised quadrangles. | contribution 0.93 | 0.92 | 0.06 | asserted 0.95 |
| s1 | In particular we determine all point regular groups of automorphisms of the thick classical generalised quadrangles. | contribution 0.57 | 0.95 | 0.35 | asserted 1.00 |
| s2 | We also construct point regular groups of automorphisms of the generalised quadrangle of order $(q-1,q+1)$ obtained by Payne derivation from the classical symplectic quadrangle $\mathsf{W}(3,q)$. | contribution 0.78 | 0.94 | 0.13 | asserted 1.00 |
| s3 | For $q=p^f$ with $f\geq 2$ we obtain at least two nonisomorphic groups when $p\geq 5$ and at least three nonisomorphic groups when $p=2$ or $3$. | result 1.00 | 0.95 | 0.19 | asserted 1.00 |
| s4 | Our groups include nonabelian 2-groups, groups of exponent 9 and nonspecial $p$-groups. | result 0.98 | 0.93 | 0.12 | asserted 1.00 |
| s5 | We also enumerate all point regular groups of automorphisms of some small generalised quadrangles. | contribution 0.78 | 0.94 | 0.07 | asserted 1.00 |
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Original abstract
We study the point regular groups of automorphisms of some of the known generalised quadrangles. In particular we determine all point regular groups of automorphisms of the thick classical generalised quadrangles. We also construct point regular groups of automorphisms of the generalised quadrangle of order $(q-1,q+1)$ obtained by Payne derivation from the classical symplectic quadrangle $\mathsf{W}(3,q)$. For $q=p^f$ with $f\geq 2$ we obtain at least two nonisomorphic groups when $p\geq 5$ and at least three nonisomorphic groups when $p=2$ or $3$. Our groups include nonabelian 2-groups, groups of exponent 9 and nonspecial $p$-groups. We also enumerate all point regular groups of automorphisms of some small generalised quadrangles.
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