The Probabilistic Zeta Function of the Alternating Group
Bollettino dell'Unione Matematica Italiana (2007)
- Volume: 10-B, Issue: 3, page 581-591
- ISSN: 0392-4041
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topMassa, Marilena. "The Probabilistic Zeta Function of the Alternating Group $\operatorname{Alt} (p + 1)$." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 581-591. <http://eudml.org/doc/290407>.
@article{Massa2007,
abstract = {We study the irreducibility of the Dirichlet polynomial $P_G(s)$ when $G$ is the alternating group on $p + 1$ elements with $p$ prime and we prove that $P_G(s)$ is irreducible for infinitely many choiches of $p$.},
author = {Massa, Marilena},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {581-591},
publisher = {Unione Matematica Italiana},
title = {The Probabilistic Zeta Function of the Alternating Group $\operatorname\{Alt\} (p + 1)$},
url = {http://eudml.org/doc/290407},
volume = {10-B},
year = {2007},
}
TY - JOUR
AU - Massa, Marilena
TI - The Probabilistic Zeta Function of the Alternating Group $\operatorname{Alt} (p + 1)$
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 581
EP - 591
AB - We study the irreducibility of the Dirichlet polynomial $P_G(s)$ when $G$ is the alternating group on $p + 1$ elements with $p$ prime and we prove that $P_G(s)$ is irreducible for infinitely many choiches of $p$.
LA - eng
UR - http://eudml.org/doc/290407
ER -
References
top- ALLADI, K. - SOLOMON, R. - TURULL, A., Finite simple groups of bounded subgroup chain length, J. Algebra, 231 (2000), 374-386. Zbl0962.20014MR1779605DOI10.1006/jabr.2000.8371
- BOSTON, NIGEL, A probabilistic generalization of the Riemann zeta function, Analytic number theory, Vol. 1 (Allerton Park, IL, 1995) 138 (1996), 155-162. Zbl0853.11075MR1399336
- BROWN, KENNETH S., The coset poset and probabilistic zeta function of a finite group, J. Algebra, 225, no. 2 (2000), 989-1012. Zbl0973.20016MR1741574DOI10.1006/jabr.1999.8221
- DAMIAN, ERIKA ANDREA, - LUCCHINI FIORENZA, - MORINI, Some properties of the probabilistic zeta function of finite simple groups, Pacific J. Math., 215 (2004), 3-14. Zbl1113.20063MR2060491DOI10.2140/pjm.2004.215.3
- DIXON, JOHN D. - MORTIMER, BRIAN, Permutation groups, Graduate Texts in Mathematics, vol. 163, Springer-Verlag, New York, 1996. Zbl0951.20001MR1409812DOI10.1007/978-1-4612-0731-3
- HALL, PHILIP, The eulerian functions of a group, Quart. J. Math., no. 7 (1936), 134-151. Zbl0014.10402
- HARDY, G. H. - WRIGHT, E. M., An introduction to the theory of numbers, fifth ed., The Clarendon Press Oxford University Press, New York, 1979. Zbl0423.10001MR568909
- MANN, AVINOAM, Positively finitely generated groups, Forum Math.8, no. 4 (1996), 429-459. Zbl0852.20019MR1393323DOI10.1515/form.1996.8.429
- RIBENBOIM, P., The New Book of Prime Number Records, Springer-Verlag, New York, 1989, 23-24. MR1016815DOI10.1007/978-1-4684-0507-1
- SHARESHIAN, JOHN, On the probabilistic zeta function for finite groups, J. Algebra210, no. 2 (1998), 703-707. Zbl1013.11058MR1662324DOI10.1006/jabr.1998.7560
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