✦ LIBER ✦

On Sylow Subgroups of Local Galois-Groups

✍ Scribed by S. Liedahl

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 517 KB
Volume: 173
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1995.1098

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✦ Synopsis

Let (p) be an odd prime, and let (\mathscr{P}) denote the class of (p)-groups which occur as Sylow (p)-subgroups of finite Galois groups over the (p)-adic field (Q_{p}). We prove that (\mathscr{P}) contains every abelian (p)-group of rank (\leq(p-1)^{2}), and that certain nonabelian (p)-groups do not belong to (\mathscr{P}). For certain number fields (K), we show that (\mathscr{P}) coincides with the class of Sylow p-subgroups of (K)-admissible groups. @ 1995 Academic Press, Inc.

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