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Given a prime number p , every irreducible character χ of a finite group G determines a unique conjugacy class of p -subgroups of G which we will call the anchors of χ . This invariant has been considered by Barker in the context of finite p -solvable groups. Besides proving some basic properties of these anchors, we investigate the relation to other p -groups which can be attached to irreducible characters, such as defect groups, vertices in the sense of J.A. Green and vertices in the sense of G. Navarro. [ABSTRACT FROM AUTHOR]

Abstract: Let n and k be positive integers. We consider the (ordinary) depth of several Young subgroups of the symmetric group . For , has depth in . Moreover, for , we show that the depth of in is in case , and it is if . For , we give upper and lower bounds for the depth. Furthermore, we give the precise values for and . [Copyright &y& Elsevier]

Abstract: In this article we determine the vertices and sources of the basic spin module for the symmetric group of degree over a field of characteristic 2. [Copyright &y& Elsevier]

Abstract: We present some algorithmic methods for the computation of vertices of indecomposable and simple modules over group algebras in prime characteristic. Furthermore, we apply these to the simple modules of the symmetric groups and determine the vertices of all simple modules of the symmetric groups of degree at most 14 and 15 in characteristic 2 and 3, respectively, with one exception. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate certain ideals in the center of a symmetric algebra A over an algebraically closed field of characteristic . These ideals include the Higman ideal and the Reynolds ideal. They are closely related to the p-power map on A. We generalize some results concerning these ideals from group algebras to symmetric algebras, and we obtain some new results as well. In case , these ideals detect odd diagonal entries in the Cartan matrix of A. In a sequel to this paper, we will apply our results to group algebras. [Copyright &y& Elsevier]

Abstract: In this paper we investigate general properties of Cartan invariants of a finite group G in characteristic 2. One of our results shows that the Cartan matrix of G in characteristic 2 contains an odd diagonal entry if and only if G contains a real element of 2-defect zero. We also apply these results to 2-blocks of symmetric groups and to blocks with normal or abelian defect groups. The second part of the paper deals with annihilators of certain ideals in centers of group algebras and blocks. [Copyright &y& Elsevier]