1990
DOI: 10.1016/0021-8693(90)90144-d
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Cited by 5 publications
(7 citation statements)
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“…Section 2 presents several general results that are required in Sect. 3. We complete this Section by observing that [1, Theorem 1.2], a result in this context for p-solvable finite groups, involves the concept of a vertex pair of Sibley in [9,Definition 2.6]. In order to prove that [1, Theorem 2] is a consequence of Theorem 1.1, we require two preliminary results:…”
Section: Introduction and Statements Of Resultsmentioning
confidence: 99%
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“…Section 2 presents several general results that are required in Sect. 3. We complete this Section by observing that [1, Theorem 1.2], a result in this context for p-solvable finite groups, involves the concept of a vertex pair of Sibley in [9,Definition 2.6]. In order to prove that [1, Theorem 2] is a consequence of Theorem 1.1, we require two preliminary results:…”
Section: Introduction and Statements Of Resultsmentioning
confidence: 99%
“…Then (P, u) is a self-centralizing vertex pair for each u ∈ C. Corollary 1.6. Theorem 1.2 of[9] is a consequence of Theorem 1.1.…”
mentioning
confidence: 98%
“…The following properties of vertex subpairs and sources are closer to the approach of [15]. (i) There exists a primitive idempotent i of the algebra (OG) P such thatē P br P (i) = 0 and that M is isomorphic to a direct summand of the OGe-module OGi ⊗ OP V .…”
Section: Vertex Subpairs and The Green Correspondencementioning
confidence: 99%
“…In Sections 1 and 2, we review the theory of subpairs that has been defined in [1]. Then we refine the definition of the Brauer functor, as well as Green's theory of vertices and sources (following [15]) to take subpairs into consideration. In Section 3, we define the notion of a Brauer-friendly module.…”
Section: Introductionmentioning
confidence: 99%
“…This section gathers definitions and results from [1], [23] and [4]. Notice that the latter reference uses a functorial approach that we do not need here.…”
Section: Brauer-friendly Modules and The Slash Constructionmentioning
confidence: 99%