A finiteness condition on the coefficients of the probabilistic Zeta function

Duong Hoang Dung; Andrea Lucchini

A finiteness condition on the coefficients of the probabilistic Zeta function

Duong Hoang Dung, Andrea Lucchini

Research output: Contribution to journal › Article › peer-review

Abstract

We discuss whether finiteness properties of a profinite group G can be deduced from the coeffcients of the probabilistic zeta function P_G(s). In particular we prove that if P_G(s) is rational and all but finitely many non abelian composition factors of G are isomorphic to PSL(2; p) for some prime p, then G contains only finitely many maximal subgroups.

Original language	English
Pages (from-to)	167-174
Number of pages	8
Journal	International Journal of Group Theory
Volume	2
Issue number	1
Publication status	Published - 2013
Externally published	Yes

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Cite this

@article{37bab6be6d764fe5ba90aca508584378,

title = "A finiteness condition on the coefficients of the probabilistic Zeta function",

abstract = "We discuss whether finiteness properties of a profinite group G can be deduced from the coeffcients of the probabilistic zeta function PG(s). In particular we prove that if PG(s) is rational and all but finitely many non abelian composition factors of G are isomorphic to PSL(2; p) for some prime p, then G contains only finitely many maximal subgroups.",

author = "Dung, {Duong Hoang} and Andrea Lucchini",

year = "2013",

language = "English",

volume = "2",

pages = "167--174",

journal = "International Journal of Group Theory",

issn = "2251-7650",

publisher = "University of Isfahan",

number = "1",

}

TY - JOUR

T1 - A finiteness condition on the coefficients of the probabilistic Zeta function

AU - Dung, Duong Hoang

AU - Lucchini, Andrea

PY - 2013

Y1 - 2013

N2 - We discuss whether finiteness properties of a profinite group G can be deduced from the coeffcients of the probabilistic zeta function PG(s). In particular we prove that if PG(s) is rational and all but finitely many non abelian composition factors of G are isomorphic to PSL(2; p) for some prime p, then G contains only finitely many maximal subgroups.

AB - We discuss whether finiteness properties of a profinite group G can be deduced from the coeffcients of the probabilistic zeta function PG(s). In particular we prove that if PG(s) is rational and all but finitely many non abelian composition factors of G are isomorphic to PSL(2; p) for some prime p, then G contains only finitely many maximal subgroups.

UR - http://www.scopus.com/inward/record.url?scp=84905966783&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84905966783&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84905966783

SN - 2251-7650

VL - 2

SP - 167

EP - 174

JO - International Journal of Group Theory

JF - International Journal of Group Theory

IS - 1

ER -

A finiteness condition on the coefficients of the probabilistic Zeta function

Abstract

All Science Journal Classification (ASJC) codes

Other files and links

Fingerprint

Cite this