1,975 research outputs found
Curves with more than one inner Galois point
Let be an irreducible plane curve of
where is an algebraically closed field of characteristic . A point is an inner Galois point for if
the projection from is Galois. Assume that has two
different inner Galois points and , both simple. Let and
be the respective Galois groups. Under the assumption that fixes ,
for , we provide a complete classification of and we exhibit a curve for each such . Our proof relies on deeper
results from group theory
Galois theory on the line in nonzero characteristic
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 -groups, and skew translation quadrangles of even order
We solve a fundamental question posed in Frohardt's 1988 paper [Fro] on
finite -groups with Kantor familes, by showing that finite groups with a
Kantor family having distinct members such that is a central subgroup of and the
quotient is abelian cannot exist if the center of has
exponent and the members of 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 are always
translation generalized quadrangles.Comment: 10 pages; submitted (February 2018
Compact Totally Disconnected Moufang Buildings
Let be a spherical building each of whose irreducible components is
infinite, has rank at least 2 and satisfies the Moufang condition. We show that
can be given the structure of a topological building that is compact
and totally disconnected precisely when is the building at infinity of
a locally finite affine building.Comment: To appear in Tohoku Math. Journa
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