More metanilpotent Fitting classes with bounded chief factor ranks (Q1378847)

The expressed aim of this note is to establish further examples of Fitting classes of metanilpotent groups. As still relatively little is known of Fitting classes consisting of \(p\)-groups by \(q\)-groups (\(p\), \(q\) different primes), the constructions given in this paper are of considerable importance. For their description the concept of the key section, first introduced by \textit{R. S. Dark} [Math. Z. 127, 145-156 (1972; Zbl 0234.20006)]\ is being used. For details of the constructions, the reader must be referred to the paper. All groups in the Fitting classes resulting from the constructions have the following properties: (1) their Fitting factor groups are elementary Abelian \(q\)-groups for some \(q\), (2) their nilpotent residuals are nilpotent of given class (not smaller than 3) and of exponent \(p\) or \(p^2\), (3) their \(p\)-chief factors are of ranks \(m=m(q)\) or \(1\).