ZETA FUNCTIONS OF GROUPS: EULER PRODUCTS AND SOLUBLE GROUPS

ZETA FUNCTIONS OF GROUPS: EULER PRODUCTS AND SOLUBLE GROUPS

The well-behaved Sylow theory for soluble groups is exploited to prove an Euler product for zeta functions counting certain subgroups in pro-soluble groups. This generalizes a result of Grunewald, Segal and Smith for nilpotent groups. AMS 2000 Mathematics subject classification: Primary 20F16; 11M99

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Veröffentlicht in:Proceedings of the Edinburgh Mathematical Society 2002-02, Vol.45 (1), p.149-154
1. Verfasser: du Sautoy, Marcus
Format: Artikel
Sprache:eng
Schlagworte:
Euler product
soluble group
zeta function
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Zusammenfassung:The well-behaved Sylow theory for soluble groups is exploited to prove an Euler product for zeta functions counting certain subgroups in pro-soluble groups. This generalizes a result of Grunewald, Segal and Smith for nilpotent groups. AMS 2000 Mathematics subject classification: Primary 20F16; 11M99
ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091500000456