Combinatorics
On the Largest intersecting set in ${\mathrm{GL}}_{2}\left(q\right)$ and some of its subgroups
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 497-502.

Let $q$ be a power of a prime number and $V$ be a $2$-dimensional column vector space over a finite field ${𝔽}_{q}$. Assume that ${\mathrm{SL}}_{2}\left(V\right). In this paper we prove an Erdős–Ko–Rado theorem for intersecting sets of G and we show that every maximum intersecting set of $G$ is either a coset of the stabilizer of a point or a coset of ${𝒢}_{〈w〉}$, where ${𝒢}_{〈w〉}=\left\{M\in G\phantom{\rule{0.166667em}{0ex}}:\phantom{\rule{0.166667em}{0ex}}\forall v\in V,Mv-v\in 〈w〉\right\}$, for some $w\in V\setminus \left\{0\right\}$. It is also shown that every intersecting set of $G$ is contained in a maximum intersecting set.

Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.320
Classification: 05D05,  20B35

1 Department of Industrial Engineering, Boğaziçi University, Istanbul, Turkey
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Milad Ahanjideh. On the Largest intersecting set in ${\protect \rm GL}_2(q)$ and some of its subgroups. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 497-502. doi : 10.5802/crmath.320. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.320/

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