Brauer indecomposability of Scott modules

Ishioka, Hiroki; Kunugi, Naoko

doi:10.1016/j.jalgebra.2016.09.021

Cited by 12 publications

(10 citation statements)

References 4 publications

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“…g (∆P ) for some g ∈ G. It follows that∆R ≤ Ng (∆P ) (∆Q) ≤ N G (∆Q) N ∆P (∆Q)by Lemma 3.2 of[9]. Since N ∆P (∆Q) is a vertex of M 1 , we have that M 1 (∆R) ̸ = 0.…”

mentioning

confidence: 83%

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The Brauer indecomposability of Scott modules with vertex $Q_{2^n}\times C_{2^m}$

Tuvay

2021

Hacettepe Journal of Mathematics and Statistics

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confidence: 83%

“…Since M (∆Q) is indecomposable as an N G (∆Q)-module, the fourth line of the proof of Theorem 1.3 in [9] implies that M (∆Q) = Sc(N G (∆Q), N ∆P (∆Q)), so that…”

Section: Lemma 24 Let G Be a Finite Group And Suppose Thatmentioning

confidence: 96%

The Brauer indecomposability of Scott modules with vertex $Q_{2^n}\times C_{2^m}$

Tuvay

2021

Hacettepe Journal of Mathematics and Statistics

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“…Then G has a subgroup H such that t ∈ H ∼ = S 3 . Theorem 2.2 (Theorem 1.3 of [12]). Assume that P is a p-subgroup of G and F P (G) is saturated.…”

Section: Lemma 21 ([16 Lemma 42])mentioning

confidence: 99%

The Brauer Indecomposability of Scott Modules for the Quadratic Group Qd(p)

Koshitani

Tuvay

2018

Algebr Represent Theor

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We give a sufficient condition for the kG-Scott module with vertex P to remain indecomposable under taking the Brauer construction for any subgroup Q of P as k[Q C G (Q)]-module, where k is a field of characteristic 2, and P is a wreathed 2subgroup of a finite group G. This generalizes results for the cases where P is abelian and some others. The motivation of this paper is that the Brauer indecomposability of a p-permutation bimodule (p is a prime) is one of the key steps in order to obtain a splendid stable equivalence of Morita type by making use of the gluing method that then can possibly lift to a splendid derived equivalence.

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“…Hence, for a fixed i, a vertex of M i is contained in Nh ∆P (∆Q). Note that for such h, we have thatNh ∆P (∆Q) ≤ N H (∆Q) ∆Sby Lemma 3.2 of[9]. So for a fixed i, any vertex of M i is contained in ∆S.…”

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confidence: 91%

The Brauer indecomposability of Scott modules with semidihedral vertex

Koshitani,

Tuvay

2019

Preprint

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We present a sufficient condition for the kG-Scott module with vertex P to remain indecomposable under the Brauer construction for any subgroupwhere k is a field of characteristic 2, and P is a semidihedral 2-subgroup of a finite group G. This generalizes results for the cases where P is abelian or dihedral. The Brauer indecomposability is defined by R. Kessar, N. Kunugi and N. Mitsuhashi. The motivation of this paper is a fact that the Brauer indecomposability of a ppermutation bimodule (p is a prime) is one of the key steps in order to obtain a splendid stable equivalence of Morita type by making use of the gluing method due to Broué, Rickard, Linckelmann and Rouquier, that then can possibly be lifted to a splendid derived (splendid Morita) equivalence.

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Brauer indecomposability of Scott modules

Cited by 12 publications

References 4 publications

The Brauer indecomposability of Scott modules with vertex $Q_{2^n}\times C_{2^m}$

The Brauer indecomposability of Scott modules with vertex $Q_{2^n}\times C_{2^m}$

The Brauer Indecomposability of Scott Modules for the Quadratic Group Qd(p)

The Brauer indecomposability of Scott modules with semidihedral vertex

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