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Comptes Rendus. Mathématique
Combinatorics
On the Largest intersecting set in GL 2 (q) 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 SL 2 (V)<GGL 2 (V). 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 ={MG:vV,Mv-vw}, for some wV{0}. It is also shown that every intersecting set of G is contained in a maximum intersecting set.

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Accepted:
Published online:
DOI: 10.5802/crmath.320
Classification: 05D05,  20B35
Milad Ahanjideh 1

1 Department of Industrial Engineering, Boğaziçi University, Istanbul, Turkey
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     author = {Milad Ahanjideh},
     title = {On the {Largest} intersecting set in ${\protect \rm GL}_2(q)$ and some of its subgroups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {497--502},
     publisher = {Acad\'emie des sciences, Paris},
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     year = {2022},
     doi = {10.5802/crmath.320},
     language = {en},
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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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