منابع مشابه
On 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 کاملDefect of characters of the symmetric group
Following the work of B. Külshammer, J. B. Olsson and G. R. Robinson on generalized blocks of the symmetric groups, we give a definition for the l-defect of characters of the symmetric group Sn, where l > 1 is an arbitrary integer. We prove that the l-defect is given by an analogue of the hook-length formula, and use it to prove, when n < l, an l-version of the McKay Conjecture in Sn.
متن کاملVertices of Specht Modules and Blocks of the Symmetric Group
This paper studies the vertices, in the sense defined by J. A. Green, of Specht modules for symmetric groups. The main theorem gives, for each indecomposable non-projective Specht module, a large subgroup contained in one of its vertices. A corollary of this theorem is a new way to determine the defect groups of symmetric groups. The main theorem is also used to find the Green correspondents of...
متن کاملOn blocks with abelian defect groups of small rank
Let B be a p-block of a finite group with abelian defect group D. Suppose that D has no elementary abelian direct summand of order p. Then we show that B satisfies Brauer’s k(B)-Conjecture (i. e. k(B) ≤ |D|). Together with former results, it follows that Brauer’s k(B)-Conjecture holds for all blocks of defect at most 3. We also obtain some related results.
متن کاملA characterization of the symmetric group of prime degree
Let $G$ be a finite group and $Gamma(G)$ the prime graph of $G$. Recently people have been using prime graphs to study simple groups. Naturally we pose a question: can we use prime graphs to study almost simple groups or non-simple groups? In this paper some results in this respect are obtained and as follows: $Gcong S_p$ if and only if $|G|=|S_p|$ and $Gamma(G)=Gamma(S_p)$, whe...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2004
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2004.04.006