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Cyclic Quotients of Transitive Groups

✍ Scribed by Robert M. Guralnick

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
170 KB
Volume
234
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

this paper is dedicated to helmut wielandt on the occasion of his 90th birthday

Let A be a transitive subgroup of S n . We show that the largest cyclic quotient of A has order at most n. This can be interpreted as an equivalent result about extensions of constants in the Galois closure of a covering of curves over a finite field. We also prove that the point stabilizer in a finite primitive permutation group always has a faithful orbit.

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