Geodesic
Normally $\zeta$-reversible profinite groups
Algebra and discrete mathematics, Tome 21 (2016) no. 1, pp. 24-50

Voir la notice de l'article provenant de la source Math-Net.Ru

We examine (finitely generated) profinite groups in which two formal Dirichlet series, the normal subgroup zeta function and the normal probabilistic zeta function, coincide; we call these groups normally $\zeta$-reversible. We conjecture that these groups are pronilpotent and we prove this conjecture if $G$ is a normally $\zeta$-reversible satisfying one of the following properties: $G$ is prosoluble, $G$ is perfect, all the nonabelian composition factors of $G$ are alternating groups.
Keywords: profinite groups, Dirichlet series. 
@article{ADM_2016_21_1_a3,
     author = {Leone Cimetta and Andrea Lucchini},
     title = {Normally $\zeta$-reversible profinite groups},
     journal = {Algebra and discrete mathematics},
     pages = {24--50},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2016_21_1_a3/}
}
TY  - JOUR
AU  - Leone Cimetta
AU  - Andrea Lucchini
TI  - Normally $\zeta$-reversible profinite groups
JO  - Algebra and discrete mathematics
PY  - 2016
SP  - 24
EP  - 50
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2016_21_1_a3/
LA  - en
ID  - ADM_2016_21_1_a3
ER  - 
%0 Journal Article
%A Leone Cimetta
%A Andrea Lucchini
%T Normally $\zeta$-reversible profinite groups
%J Algebra and discrete mathematics
%D 2016
%P 24-50
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2016_21_1_a3/
%G en
%F ADM_2016_21_1_a3
Leone Cimetta; Andrea Lucchini. Normally $\zeta$-reversible profinite groups. Algebra and discrete mathematics, Tome 21 (2016) no. 1, pp. 24-50. http://geodesic.mathdoc.fr/item/ADM_2016_21_1_a3/