On the (non-)contractibility of the order complex of the coset poset of an alternating group

Massimiliano Patassini

Rendiconti del Seminario Matematico della Università di Padova (2013)

  • Volume: 129, page 35-46
  • ISSN: 0041-8994

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Patassini, Massimiliano. "On the (non-)contractibility of the order complex of the coset poset of an alternating group." Rendiconti del Seminario Matematico della Università di Padova 129 (2013): 35-46. <http://eudml.org/doc/275108>.

@article{Patassini2013,
author = {Patassini, Massimiliano},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {probabilistic zeta functions; simplicial complexes; order complexes; contractibility; coset posets; alternating groups; Brown conjecture},
language = {eng},
pages = {35-46},
publisher = {Seminario Matematico of the University of Padua},
title = {On the (non-)contractibility of the order complex of the coset poset of an alternating group},
url = {http://eudml.org/doc/275108},
volume = {129},
year = {2013},
}

TY - JOUR
AU - Patassini, Massimiliano
TI - On the (non-)contractibility of the order complex of the coset poset of an alternating group
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2013
PB - Seminario Matematico of the University of Padua
VL - 129
SP - 35
EP - 46
LA - eng
KW - probabilistic zeta functions; simplicial complexes; order complexes; contractibility; coset posets; alternating groups; Brown conjecture
UR - http://eudml.org/doc/275108
ER -

References

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  1. [1] N. Boston, A probabilistic generalization of the Riemann zeta function, Analytic Number Theory, 1 (1996), pp. 155–162. Zbl0853.11075MR1399336
  2. [2] K. S. Brown, The coset poset and the probabilistic zeta function of a finite group, J. Algebra, 225 (2000), pp. 989–1012. Zbl0973.20016MR1741574
  3. [3] E. Detomi - A. Lucchini, Crowns and factorization of the probabilistic zeta function of a finite group, J. Algebra, 265 (2003), pp. 651–668. Zbl1072.20031MR1987022
  4. [4] W. Gaschütz, Zu einem von B. H. und H. Neumann gestellten Problem, Math. Nachr., 14 (1955), pp. 249–252. MR83993
  5. [5] T. Hawkes - M. Isaacs - M. Õzaydin, On the Möbius function of a finite group, Rocky Mountain Journal, 19 (1989), pp. 1003–1034. Zbl0708.20005MR1039540
  6. [6] A. Mann, Positively finitely generated groups, Forum Math., 8 (1996), pp. 429–459. Zbl0852.20019MR1393323
  7. [7] M. Patassini, The Probabilistic Zeta function of P S L 2 ( q ) , of the Suzuki groups 2 B 2 ( q ) and of the Ree groups 2 G 2 ( q ) , Pacific J. Math., 240 (2009), pp. 185–200. Zbl1167.20013MR2485479
  8. [8] M. Patassini, On the Dirichlet polynomial of the simple group of Lie type, Università di Padova, 2011, http://paduaresearch.cab.unipd.it/3272/1/Phd_Thesis.pdf, Zbl1260.20030
  9. [9] M. Patassini, On the (non-)contractibility of the order complex of the coset poset of a classical group, J. Algebra, 343 (2011), pp. 37–77. Zbl1242.20026MR2824544
  10. [10] M. Patassini, Recognizing the non-Frattini abelian chief factors of a finite group from its Probabilistic Zeta function, Accepted by Comm. Algeb., 2011. Zbl1268.20023MR2989660
  11. [11] P. Jiménez Seral, Coefficient of the Probabilistic Zeta function of a monolithic group, Glasgow J. Math., 50 (2008), pp. 75–81. MR2381734

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