We show that two metacyclic groups of the following types are isomorphic if they have the same character tables: (i) split metacyclic groups, (ii) the metacyclic p-groups and (iii) the metacyclic {p, q}-groups, where p, q are odd primes. 2010 Mathematics Subject Classification. Primary 20C15; Secondary 20D15, 20F16, 20F22.

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...

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 ...

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.