A stronger reformulation of Webb's conjecture in terms of finite topological spaces
We investigate a stronger formulation of Webb's conjecture on the contractibility of the orbit space of the p-subgroup complexes in terms of finite topological spaces. The original conjecture, which was first proved by Symonds and, more recently, by Bux, Libman and Linckelmann, can be restated...
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Academic Press Inc.
2019
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| 003 | AR-BaUEN | ||
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| 008 | 190410s2019 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-85062996904 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 030 | |a JALGA | ||
| 100 | 1 | |a Piterman, K.I. | |
| 245 | 1 | 2 | |a A stronger reformulation of Webb's conjecture in terms of finite topological spaces |
| 260 | |b Academic Press Inc. |c 2019 | ||
| 506 | |2 openaire |e Política editorial | ||
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| 504 | |a Craven, D.A., The Theory Of Fusion Systems: an Algebraic Approach (2011) Cambridge Studies in Advanced Mathematics, 131. , Cambridge University Press Cambridge xii+371 pp | ||
| 504 | |a (2016), A. Díaz Ramos, On Quillen's conjecture for p-solvable groups, preprint; GAP – Groups, Algorithms, and Programming (2014), http://www.gap-system.org, Version 4.7.6; Hawkes, T., Isaacs, I.M., On the poset of p-subgroups of a p-solvable group (1988) J. Lond. Math. Soc. (2), 38 (1), pp. 77-86 | ||
| 504 | |a Ksontini, R., Simple connectivity of the Quillen complex of the symmetric group (2003) J. Combin. Theory Ser. A, 103, pp. 257-279 | ||
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| 504 | |a Libman, A., Webb's conjecture for fusion systems (2008) Israel J. Math., 167, pp. 141-154 | ||
| 504 | |a Linckelmann, M., The orbit space of a fusion system is contractible (2009) Proc. Lond. Math. Soc. (3), 98, pp. 191-216 | ||
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| 504 | |a Minian, E.G., Piterman, K.I., The homotopy types of the posets of p-subgroups of a finite group (2018) Adv. Math., 328, pp. 1217-1233 | ||
| 504 | |a Quillen, D., Homotopy properties of the poset of nontrivial p-subgroups of a group (1978) Adv. Math., 28, pp. 101-128 | ||
| 504 | |a SageMath, the Sage Mathematics Software System (2016), http://www.sagemath.org, Version 7.6, the Sage Developers; Smith, S.D., Subgroup Complexes (2011) Mathematical Surveys and Monographs, 179. , Amer. Math. Soc. Providence, RI xii+364 | ||
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| 504 | |a Symonds, P., The orbit space of the p-subgroup complex is contractible (1998) Comment. Math. Helv., 73 (3), pp. 400-405 | ||
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| 504 | |a Webb, P.J., Subgroup complexes (1987) The Arcata Conference on Representations of Finite Groups, Arcata, Calif., 1986, Proc. Sympos. Pure Math., 47, pp. 349-365. , Amer. Math. Soc. Providence, RI | ||
| 520 | 3 | |a We investigate a stronger formulation of Webb's conjecture on the contractibility of the orbit space of the p-subgroup complexes in terms of finite topological spaces. The original conjecture, which was first proved by Symonds and, more recently, by Bux, Libman and Linckelmann, can be restated in terms of the topology of certain finite spaces. We propose a stronger conjecture, and prove various particular cases by combining fusion theory of finite groups and homotopy theory of finite spaces. © 2019 Elsevier Inc. |l eng | |
| 593 | |a Departamento de Matemática, IMAS-CONICET, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a FINITE TOPOLOGICAL SPACES |
| 690 | 1 | 0 | |a ORBIT SPACES |
| 690 | 1 | 0 | |a P-SUBGROUPS |
| 690 | 1 | 0 | |a POSETS |
| 650 | 1 | 7 | |2 spines |a FUSION |
| 773 | 0 | |d Academic Press Inc., 2019 |g v. 527 |h pp. 280-305 |p J. Algebra |x 00218693 |w (AR-BaUEN)CENRE-221 |t Journal of Algebra | |
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| 856 | 4 | 0 | |u https://doi.org/10.1016/j.jalgebra.2019.02.037 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00218693_v527_n_p280_Piterman |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v527_n_p280_Piterman |y Registro en la Biblioteca Digital |
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