In [4], Cameron and Cara showed a relationship between independent generating sets of a group G and RWPri geometries for G. We first notice a connection between such independent generating sets in G and those in the quotient G/Φ(G), where Φ(G) is the Frattini subgroup of G. This suggests a similar connection for RWPri geometries. We prove that there is a one-to-one correspondence between the RW...

The notions of nearly-maximal and near Frattini subgroups considered by J.B. Riles in [20] and the natural related notions are characterized for abelian groups.

The availability of some supplementary cementitious materials, especially fly ash, is imminent concern in Europe due to the projected closure several coal-fired power generation plants. Pure kaolinitic clays, which arguably have potential replace are also scarce and expensive their use other industrial applications. This paper examines utilisation low-grade clays for construction purposes. clay...

We prove that for any prime number p, every finite non-abelian p-group G of class 2 has a noninner automorphism of order p leaving either the Frattini subgroup Φ(G) or Ω1(Z(G)) elementwise fixed.

Many common finite p-groups admit automorphisms of order coprime to p, and when p is odd, it is reasonably difficult to find finite p-groups with automorphism group a p-group. Yet the goal of this paper is to prove that almost all finite p-groups do have automorphism group a p-group when p is odd. The asymptotic sense in which the theorem holds involves bounding the Frattini length of the p-gro...

We prove that the number of groups of order p whose Frattini subgroup is central is for fixed n a PORC (‘polynomial on residue classes’) function of p. This extends a result of G. Higman.