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Galois number fields with small root discriminant

โœ Scribed by John W. Jones; David P. Roberts


Book ID
104024733
Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
318 KB
Volume
122
Category
Article
ISSN
0022-314X

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โœฆ Synopsis


We pose the problem of identifying the set K(G, ฮฉ) of Galois number fields with given Galois group G and root discriminant less than the Serre constant ฮฉ โ‰ˆ 44.7632. We definitively treat the cases G = A 4 , A 5 , A 6 and S 4 , S 5 , S 6 , finding exactly 59, 78, 5 and 527, 192, 13 fields, respectively. We present other fields with Galois group SL 3 (2), A 7 , S 7 , PGL 2 (7), SL 2 (8), ฮฃL 2 (8), PGL 2 (9), Pฮ“ L 2 (9), PSL 2 (11), and A 2 5 .2, and root discriminant less than ฮฉ. We conjecture that for all but finitely many groups G, the set K(G, ฮฉ) is empty.


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