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Galois Groups of Trinomials

โœ Scribed by S.D Cohen; A Movahhedi; A Salinier

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
113 KB
Volume
222
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

Galois groups of irreducible trinomials X n + aX s + b โˆˆ X are investigated assuming the classification of finite simple groups. We show that under some simple yet general hypotheses bearing on the integers n s a and b only very specific groups can occur. For instance, if the two integers nb and as n -s are coprime and if s is a prime number, then already the Galois group of f X is either the alternating group A n or the symmetric group S n . This significantly extends work of Osada.

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