## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Near polygons having a big sub near polygon isomorphic to $\mathbb G_n$

Bart De Bruyn

#### Abstract

In [7] a new infinite class $\mathbb G_n$, $n \geq 0$, of near polygons was defined. The near $2n$-gon $\mathbb G_n$ has the property that it contains $\mathbb G_{n-1}$ as a big geodetically closed sub near polygon. In this paper, we determine all near $2n$-gons, $n \geq 4$, having $\mathbb G_{n-1}$ as a big geodetically closed sub near $2(n-1)$-gon under the additional assumption that every two points at distance 2 have at least two common neighbours. We will prove that such a near $2n$-gon is isomorphic to either $\mathbb G_n$, $\mathbb G_{n-1} \otimes \mathbb G_2$, or $\mathbb G_{n-1} \times L$ for some line $L$.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 11, Number 3 (2004), 321-341.

Dates
First available in Project Euclid: 24 August 2004

https://projecteuclid.org/euclid.bbms/1093351376

Digital Object Identifier
doi:10.36045/bbms/1093351376

Mathematical Reviews number (MathSciNet)
MR2098411

Zentralblatt MATH identifier
1067.05016

#### Citation

De Bruyn, Bart. Near polygons having a big sub near polygon isomorphic to $\mathbb G_n$. Bull. Belg. Math. Soc. Simon Stevin 11 (2004), no. 3, 321--341. doi:10.36045/bbms/1093351376. https://projecteuclid.org/euclid.bbms/1093351376