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ZETA FUNCTIONS OF GROUPS: EULER PRODUCTS AND SOLUBLE GROUPS

Published online by Cambridge University Press:  05 February 2002

Marcus du Sautoy
Marcus du Sautoy
Affiliation:
Mathematical Institute, 24–29 St Giles, Oxford OX1 3LB, UK ([email protected])
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Abstract

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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

Keywords

zeta functionsoluble groupEuler product
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 1 , February 2002 , pp. 149 - 154
Copyright
Copyright © Edinburgh Mathematical Society 2002