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- W2221207038 abstract "We consider the action of the $2$-dimensional projective general linear group $PGL(2,q)$ on the projective line $PG(1,q)$. A subset $S$ of $PGL(2,q)$ is said to be an intersecting family if for every $g_1,g_2 in S$, there exists $alpha in PG(1,q)$ such that $alpha^{g_1}= alpha^{g_2}$. It was proved by Meagher and Spiga that the intersecting families of maximum size in $PGL(2,q)$ are precisely the cosets of point stabilizers. We prove that if an intersecting family $S subset PGL(2,q)$ has size close to the maximum then it must be close in structure to a coset of a point stabilizer. This phenomenon is known as stability. We use this stability result proved here to show that if the size of $S$ is close enough to the maximum then $S$ must be contained in a coset of a point stabilizer." @default.
- W2221207038 created "2016-06-24" @default.
- W2221207038 creator A5080929585 @default.
- W2221207038 date "2015-12-23" @default.
- W2221207038 modified "2023-09-23" @default.
- W2221207038 title "Stability for Intersecting Families in PGL(2,q)" @default.
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- W2221207038 doi "https://doi.org/10.37236/5401" @default.
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