1,975 research outputs found

    Curves with more than one inner Galois point

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    Let C\mathcal{C} be an irreducible plane curve of PG(2,K)\text{PG}(2,\mathbb{K}) where K\mathbb{K} is an algebraically closed field of characteristic p≥0p\geq 0. A point Q∈CQ\in \mathcal{C} is an inner Galois point for C\mathcal{C} if the projection πQ\pi_Q from QQ is Galois. Assume that C\mathcal{C} has two different inner Galois points Q1Q_1 and Q2Q_2, both simple. Let G1G_1 and G2G_2 be the respective Galois groups. Under the assumption that GiG_i fixes QiQ_i, for i=1,2i=1,2, we provide a complete classification of G=⟨G1,G2⟩G=\langle G_1,G_2 \rangle and we exhibit a curve for each such GG. Our proof relies on deeper results from group theory

    Galois theory on the line in nonzero characteristic

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    The author surveys Galois theory of function fields with non-zero caracteristic and its relation to the structure of finite permutation groups and matrix groups.Comment: 66 pages. Abstract added in migration

    A question of Frohardt on 22-groups, and skew translation quadrangles of even order

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    We solve a fundamental question posed in Frohardt's 1988 paper [Fro] on finite 22-groups with Kantor familes, by showing that finite groups with a Kantor family (F,F∗)(\mathcal{F},\mathcal{F}^*) having distinct members A,B∈FA, B \in \mathcal{F} such that A∗∩B∗A^* \cap B^* is a central subgroup of HH and the quotient H/(A∗∩B∗)H/(A^* \cap B^*) is abelian cannot exist if the center of HH has exponent 44 and the members of F\mathcal{F} are elementary abelian. In a similar way, we solve another old problem dating back to the 1970s by showing that finite skew translation quadrangles of even order (t,t)(t,t) are always translation generalized quadrangles.Comment: 10 pages; submitted (February 2018

    Compact Totally Disconnected Moufang Buildings

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    Let Δ\Delta be a spherical building each of whose irreducible components is infinite, has rank at least 2 and satisfies the Moufang condition. We show that Δ\Delta can be given the structure of a topological building that is compact and totally disconnected precisely when Δ\Delta is the building at infinity of a locally finite affine building.Comment: To appear in Tohoku Math. Journa
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