Abstract. Let K be a field of characteristic p and G a nonabelian metacyclic finite p-group. We give an explicit list of all metacyclic p-groups G, such that the group algebra KG over a field of characteristic p has a filtered multiplicative K-basis. We also present an example of a non-metacyclic 2-group G, such that the group algebra KG over any field of characteristic 2 has a filtered multipl...

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 ...

A finite p-group S is said to be of supersoluble type if every fusion system over supersoluble. The main aim this paper characterise the p-groups type. Abelian and metacyclic are completely described. Furthermore, we show that Sylow p-subgroups a simple group must cyclic.

A complete characterization of locally primitive normal Cayley graphs of metacyclic groups is given. Namely, let Γ = Cay(G,S) be such a graph, where G ∼= Zm.Zn is a metacyclic group and m = p1 1 p r2 2 · · · p rt t such that p1 < p2 < · · · < pt. It is proved that G ∼= D2m is a dihedral group, and val(Γ ) = p is a prime such that p|(p1(p1 − 1), p2 − 1, . . . , pt − 1). Moreover, three types of ...