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Duong, Hoang Dung, Lucchini, Andrea. (1391). A finiteness condition on the coefficients of the probabilistic zeta function. , 2(1), 167-174. doi: 10.22108/ijgt.2013.2760
Hoang Dung Duong; Andrea Lucchini. "A finiteness condition on the coefficients of the probabilistic zeta function". , 2, 1, 1391, 167-174. doi: 10.22108/ijgt.2013.2760
Duong, Hoang Dung, Lucchini, Andrea. (1391). 'A finiteness condition on the coefficients of the probabilistic zeta function', , 2(1), pp. 167-174. doi: 10.22108/ijgt.2013.2760
Duong, Hoang Dung, Lucchini, Andrea. A finiteness condition on the coefficients of the probabilistic zeta function. , 1391; 2(1): 167-174. doi: 10.22108/ijgt.2013.2760

A finiteness condition on the coefficients of the probabilistic zeta function

International Journal of Group Theory
مقاله 14، دوره 2، شماره 1، خرداد 2013، صفحه 167-174    اصل مقاله (291.54 K)
نوع مقاله: Ischia Group Theory 2012
شناسه دیجیتال (DOI): 10.22108/ijgt.2013.2760
نویسندگان
Hoang Dung Duong1؛ Andrea Lucchini* 2
1Mathematisch Instituut, Leiden Universiteit, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
2Dipartimento di Matematica Università di Padova
چکیده
We discuss whether finiteness properties of a profinite group $G$ can be deduced from the coefficients 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.
کلیدواژه‌ها
Probabilistic zeta function؛ finiteness conditions؛ special linear groups
مراجع
L. E. Dickson (1958) Linear groups: With an exposition of the Galois field theory Dover Publications Inc., New York
E. Detomi and A. Lucchini (2003) Crowns and factorization of the probabilistic zeta function of a finite group J. Algebra 265 (2), 651-668
E. Detomi and A. Lucchini (2006) Crowns in profinite groups and applications Noncommutative algebra and geometry, Lect. Notes Pure Appl. Math., Chapman \& Hall/CRC, Boca Raton, FL 243, 47-62
E. Detomi and A. Lucchini (2006) Profinite groups with a rational probabilistic zeta function J. Group Theory 9 (2), 203-217
E. Detomi and A. Lucchini (2007) Non-prosoluble profinite groups with a rational probabilistic zeta function J. Group Theory 10 (4), 453-466
D. H. Duong and A. Lucchini Rationality of the probabilistic zeta function of finitely generated profinite groups preprint
P.~J. Seral (2008) Coefficient of the probabilistic zeta function of a monolithic group Glasgow J. Math. 50, 75-81
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