Chevalley<i>p</i>–local finite groups

Broto, Carles; Møller, Jesper M.

doi:10.2140/agt.2007.7.1809

Cited by 27 publications

(39 citation statements)

References 67 publications

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“…Unlike the other known infinite families of exotic p-local finite groups [13,30], some of these new families cannot be constructed as the homotopy fixed points of automorphism of a p-compact group. Nevertheless, it is still possible to construct an "ascending" chain of exotic p-local finite groups whose colimit, we conjecture, should provide an example of an exotic p-local compact group [12,Section 6].…”

Section: Theorem 11 Let P Be An Odd Prime and Let S Be A Rank Two Pmentioning

confidence: 99%

All 𝑝-local finite groups of rank two for odd prime 𝑝

Díaz

Ruiz

Viruel³

2006

Trans. Amer. Math. Soc.

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Abstract. In this paper we give a classification of the rank two p-local finite groups for odd p. This study requires the analysis of the possible saturated fusion systems in terms of the outer automorphism group of the possible Fradical subgroups. Also, for each case in the classification, either we give a finite group with the corresponding fusion system or we check that it corresponds to an exotic p-local finite group, getting some new examples of these for p = 3.

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Section: Theorem 11 Let P Be An Odd Prime and Let S Be A Rank Two Pmentioning

confidence: 99%

All 𝑝-local finite groups of rank two for odd prime 𝑝

Díaz

Ruiz

Viruel³

2006

Trans. Amer. Math. Soc.

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“…Indeed, given an unstable Adams operation ‰ acting on G , one could consider the homotopy fixed points of BG under the natural map induced by an unstable Adams operation acting on G , namely the homotopy pullback / / BG BG and apply the topological tools provided by Broto, Levi and Oliver in [5; 6] to study the homotopy type of X . This point of view is in fact closer to the work of Broto and Møller [8] mentioned above, and will constitute the main subject in a sequel of this paper, where we will relate the constructions introduced in this paper and homotopy fixed points.…”

mentioning

confidence: 55%

“…More recently, C Broto and J M Møller studied a similar construction for connected p -compact groups in [8].…”

mentioning

confidence: 99%

Unstable Adams operations acting onp–local compact groups and fixed points

Gonzalez

2012

Algebr. Geom. Topol.

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We prove that every p -local compact group is approximated by transporter systems over finite p -groups. To do so, we use unstable Adams operations acting on a given p -local compact group and study the structure of resulting fixed points. 55R35; 20D20The theory of p -local compact groups was introduced by C Broto, R Levi and B Oliver [7] as the natural generalization of p -local finite groups, also introduced by the same authors in [5], to include some infinite structures, such as compact Lie groups or p -compact groups, in an attempt to give categorical models for a larger class of p -completed classifying spaces.Nevertheless, when passing from a finite setting to an infinite one, some of the techniques used in the former case are not available any more. As a result, some of the more important results in [5] were not extended to p -local compact groups, and, roughly speaking, p -local compact groups are not yet as well understood as p -local finite groups. It is then the aim of this paper to shed some light on the new theory introduced in [7].

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“…As a consequence of the properties ofˆproved in this paper, we deduce the following result, which can be seen as a generalization of a classical theorem of de Siebenthal [33, Chapitre I, Section 2, no. 2] for compact connected Lie groups (see also Bourbaki [8,Section 4,no. 10] and Theorem 6.1).…”

Section: Introductionmentioning

confidence: 99%

“…Like for Lie groups, the theorem can be used to construct group actions and hence to construct new p -compact groups or p -local finite groups from old, using homotopy fixed point methods; see eg Dwyer and Wilkerson [16] and Broto and Møller [10].…”

Section: Introductionmentioning

confidence: 99%

Automorphisms ofp–compact groups and their root data

Andersen

Grodal

2008

Geom. Topol.

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We construct a model for the space of automorphisms of a connected p -compact group in terms of the space of automorphisms of its maximal torus normalizer and its root datum. As a consequence we show that any homomorphism to the outer automorphism group of a p -compact group can be lifted to a group action, analogous to a classical theorem of de Siebenthal for compact Lie groups. The model of this paper is used in a crucial way in our paper [2], where we prove the conjectured classification of 2-compact groups and determine their automorphism spaces. 55R35; 20G99, 22E15, 55P35

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Chevalleyp–local finite groups

Cited by 27 publications

References 67 publications

All 𝑝-local finite groups of rank two for odd prime 𝑝

All 𝑝-local finite groups of rank two for odd prime 𝑝

Unstable Adams operations acting onp–local compact groups and fixed points

Automorphisms ofp–compact groups and their root data

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