منابع مشابه
The Dade group of a metacyclic p-group
The Dade group D(P ) of a finite p-group P , formed by equivalence classes of endopermutation modules, is a finitely generated abelian group. Its torsion-free rank equals the number of conjugacy classes of non-cyclic subgroups of P and it is conjectured that every nontrivial element of its torsion subgroup D(P ) has order 2, (or also 4, in case p = 2). The group D(P ) is closely related to the ...
متن کاملA sectional characterization of the Dade group
Let k be a field of characteristic p , let P be a finite pgroup, where p is an odd prime, and let D(P ) be the Dade group of endo-permutation kP -modules. It is known that D(P ) is detected via deflation–restriction by the family of all sections of P which are elementary abelian of rank ≤ 2. In this paper, we improve this result by characterizing D(P ) as the limit (with respect to deflation– r...
متن کاملTHE AUTOMORPHISM GROUP OF FINITE GRAPHS
Let G = (V,E) be a simple graph with exactly n vertices and m edges. The aim of this paper is a new method for investigating nontriviality of the automorphism group of graphs. To do this, we prove that if |E| >=[(n - 1)2/2] then |Aut(G)|>1 and |Aut(G)| is even number.
متن کاملBorel-smith Functions and the Dade Group
We show that there is an exact sequence of biset functors over p-groups 0 → Cb j −→B∗ Ψ −→D → 0 where Cb is the biset functor for the group of Borel-Smith functions, B ∗ is the dual of the Burnside ring functor, D is the functor for the subgroup of the Dade group generated by relative syzygies, and the natural transformation Ψ is the transformation recently introduced by the first author in [5]...
متن کاملOn the planarity of a graph related to the join of subgroups of a finite group
Let $G$ be a finite group which is not a cyclic $p$-group, $p$ a prime number. We define an undirected simple graph $Delta(G)$ whose vertices are the proper subgroups of $G$, which are not contained in the Frattini subgroup of $G$ and two vertices $H$ and $K$ are joined by an edge if and only if $G=langle H , Krangle$. In this paper we classify finite groups with planar graph. ...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2013
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2012.04.003