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Recognizing Soluble Groups from their Probabilistic Zeta Functions
Author(s) -
Detomi Eloisa,
Lucchini Andrea
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002297
Subject(s) - mathematics , prime (order theory) , probabilistic logic , mathematics subject classification , product (mathematics) , euler's formula , pure mathematics , combinatorics , statistics , mathematical analysis , geometry
It is proved that if P G ( s ) has an Euler product expansion with all factors of the form 1 − c i / q i Swhere each q i is a prime power, then G is soluble. 2000 Mathematics Subject Classification 20P05, 20F05, 11M41.