منابع مشابه
N ov 2 00 3 On blocks with cyclic defect group and their head orders
It is shown that [Ple83, Theorem 8.5] describes blocks of cyclic defect group up to Morita equivalence. In particular such a block is determined by its planar embedded Brauer tree. Applying the radical idealizer process the head order of such blocks is calculated explicitly.
متن کاملOn defect groups for generalized blocks of the symmetric group
In a paper of 2003, B. Külshammer, J. B. Olsson and G. R. Robinson defined l-blocks for the symmetric groups, where l > 1 is an arbitrary integer. In this paper, we give a definition for the defect group of the principal l-block. We then check that, in the Abelian case, we have an analogue of one of M. Broué’s conjectures.
متن کاملImprimitive symmetric graphs with cyclic blocks
Let Γ be a graph admitting an arc-transitive subgroup G of automorphisms that leaves invariant a vertex partition B with parts of size v ≥ 3. In this paper we study such graphs where: for B, C ∈ B connected by some edge of Γ , exactly two vertices of B lie on no edge with a vertex of C; and as C runs over all parts of B connected to B these vertex pairs (ignoring multiplicities) form a cycle. W...
متن کاملNonexistence of Graphs with Cyclic Defect
In this note we consider graphs of maximum degree ∆, diameter D and order M(∆,D) − 2, where M(∆,D) is the Moore bound, that is, graphs of defect 2. In [1] Delorme and Pineda-Villavicencio conjectured that such graphs do not exist for D ≥ 3 if they have the so called ‘cyclic defect’. Here we prove that this conjecture holds.
متن کاملOn Graphs with Cyclic Defect or Excess
The Moore bound constitutes both an upper bound on the order of a graph of maximum degree d and diameter D = k and a lower bound on the order of a graph of minimum degree d and odd girth g = 2k + 1. Graphs missing or exceeding the Moore bound by ǫ are called graphs with defect or excess ǫ, respectively. While Moore graphs (graphs with ǫ = 0) and graphs with defect or excess 1 have been characte...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1975
ISSN: 0021-8693
DOI: 10.1016/0021-8693(75)90181-7