On 2-blocks with quaternion and quasidihedral defect groups

Olsson, Jørn B.

doi:10.1016/0021-8693(75)90099-x

Cited by 83 publications

(80 citation statements)

References 11 publications

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“…Hence, the number of Ᏺ-conjugacy classes is again 2 m (2 n−1 + 1). Again D/ a 2 has maximal class and l(b a 2 ) = 2 by [Brauer 1974;Olsson 1975]. The same is true for the odd powers of a 2 .…”

Section: Bicyclic Defect Groupsmentioning

confidence: 59%

See 1 more Smart Citation

Untitled

2013

Algebra Number Theory

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We prove that limits of multiplicities associated to graded families of ideals exist under very general conditions. Most of our results hold for analytically unramified equicharacteristic local rings with perfect residue fields. We give a number of applications, including a "volume = multiplicity" formula, generalizing the formula of Lazarsfeld and Mustat ,ȃ , and a proof that the epsilon multiplicity of Ulrich and Validashti exists as a limit for ideals in rather general rings, including analytic local domains. We prove a generalization of this to generalized symbolic powers of ideals proposed by Herzog, Puthenpurakal and Verma. We also prove an asymptotic "additivity formula" for limits of multiplicities and a formula on limiting growth of valuations, which answers a question posed by the author, Kia Dalili and Olga Kashcheyeva. Our proofs are inspired by a philosophy of Okounkov for computing limits of multiplicities as the volume of a slice of an appropriate cone generated by a semigroup determined by an appropriate filtration on a family of algebraic objects.

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Section: Bicyclic Defect Groupsmentioning

confidence: 59%

“…In the second case, a similar statement is true for a 2 j . Observe that the elements xa [Brauer 1974;Olsson 1975] …”

Section: Bicyclic Defect Groupsmentioning

confidence: 99%

Untitled

2013

Algebra Number Theory

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“…This follows from an inspection of Erdmann's lists in [18,19]. By Olsson's results [23], the principal block of the group algebra kG has either 1, 2, or 3 simple modules. There is nothing to prove if there is only one simple module.…”

Section: Groups With Semi-dihedral Sylow 2-subgroupmentioning

confidence: 99%

Endotrivial modules over groups with quaternion or semi-dihedral Sylow 2-subgroup

Carlson¹,

Mazza²,

Thévenaz³

2012

J. Eur. Math. Soc.

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Abstract. Let G be a finite group with a Sylow 2-subgroup P which is either quaternion or semi-dihedral. Let k be an algebraically closed field of characteristic 2. We prove the existence of exotic endotrivial kG-modules, whose restrictions to P are isomorphic to the direct sum of the known exotic endotrivial kP -modules and some projective modules. This provides a description of the group T (G) of endotrivial kG-modules.

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“…In this notation [3, Theorem 11.1], work of Olsson [24] implies that B 1 has four characters ϑ 1 , . .…”

Section: Proof For the Block Bmentioning

confidence: 99%