The Dade group of a fusion system

Linckelmann, Markus; Mazza, Nadia

doi:10.1515/jgt.2008.060

Cited by 13 publications

(11 citation statements)

References 19 publications

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“…Moreover Note that, in particular, the computations in [21,Sect. 7.11] prove that the set of generators for D(P) PSL 3 (F p )−st computed in [22,Example 6.6] misses one generator to be complete.…”

Section: Lemma 124 Let G Be a Group With A Normal Sylow P-subgroup mentioning

confidence: 99%

The Dade group of a finite group

Lassueur

2013

Journal of Pure and Applied Algebra

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Section: Lemma 124 Let G Be a Group With A Normal Sylow P-subgroup mentioning

confidence: 99%

The Dade group of a finite group

Lassueur

2013

Journal of Pure and Applied Algebra

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“…In [20], Linckelmann and Mazza define the Dade group, D(F , P ), of a saturated fusion system F on a finite p-group P as the F -stable elements in the Dade group, D(P ), of P . Furthermore, they give a criterion for when D(F , P ) = D(P ).…”

Section: Preliminariesmentioning

confidence: 99%

Fusion systems on small 𝑝-groups

Craven

Glesser

2012

Trans. Amer. Math. Soc.

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Abstract. In this article we study several classes of 'small' 2-groups: we complete the classification, started in [26], of all saturated fusion systems on metacyclic p-groups for all primes p. We consider Suzuki 2-groups, and classify all center-free saturated fusion systems on 2-groups of 2-rank 2. We end by classifying all possible F -centric, F -radical subgroups in saturated fusion systems on 2-groups of 2-rank 2.

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“…We will need the following result. The statement on the rank is not made explicitly in [21,Proposition 3.7], and this Proposition is stated there only over k, but the slightly stronger version above follows immediately from the construction of V ′ in the proof of that Proposition in [21].…”

Section: Descent For Morita Equivalences With Endopermutation Sourcementioning

confidence: 99%

“…[21, Proposition 3.7]). Let P be a finite p-group, F a saturated fusion system on P and V and indecomposable endopermutation OP -module with vertex P such that the class of [V ] in D O (P ) is F -stable.…”

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confidence: 99%

Descent of Equivalences and Character Bijections

Kessar

Linckelmann

2018

Springer Proceedings in Mathematics &Amp; Statistics

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Categorical equivalences between block algebras of finite groupssuch as Morita and derived equivalences -are well-known to induce character bijections which commute with the Galois groups of field extensions. This is the motivation for attempting to realise known Morita and derived equivalences over non splitting fields. This article presents various results on the theme of descent to appropriate subfields and subrings. We start with the observation that perfect isometries induced by a virtual Morita equivalence induce isomorphisms of centers in non-split situations, and explain connections with Navarro's generalisation of the Alperin-McKay conjecture. We show that Rouquier's splendid Rickard complex for blocks with cyclic defect groups descends to the non-split case. We also prove a descent theorem for Morita equivalences with endopermutation source.

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The Dade group of a fusion system

Abstract: Abstract. We define the notion of the Dade group of a fusion system and show that some of the gluing and detection results for Dade groups of finite p-groups due to Bouc and Thévenaz in [8], [9] extend to Dade groups of fusion systems.

Cited by 13 publications

References 19 publications

The Dade group of a finite group

The Dade group of a finite group

Fusion systems on small 𝑝-groups

Descent of Equivalences and Character Bijections

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