Groups of prime power order. Vol. 6. (Q1646328)

The highly acclaimed five volumes on \(p\)-groups, due to the authors, were published in [Vol. 1. Berlin: Walter de Gruyter (2008; Zbl 1168.20001); Vol. 2. Berlin: Walter de Gruyter (2008; Zbl 1168.20002); Vol. 3. Berlin: Walter de Gruyter (2011; Zbl 1229.20001); Vol. 4. Berlin: De Gruyter (2016; Zbl 1344.20001); Vol. 5. Berlin: De Gruyter (2016; Zbl 1344.20002)] (see the respective reviews). To me, the reviewer of Vol. 6, its appearance came as a total surprise! There are 70 sections, presenting structure theorems of \(p\)-groups, all given with proofs. In addition, 39 so-called appendices are mentioned, i.e. once again elaborating structures of \(p\)-groups, most of them with explaining about the hows and whys. A special feature consists of 493 exercises; the reader is invited to work these out for themselves, but most of the exercises are provided with (hints to) solutions; the reviewer did find the exercises illuminating in learning by advance students to learn more about the subjects related to \(p\)-groups. Indeed, a wealth of study and a gem! Let us not forget about, what is called, ``Research problems and themes, VI''; there are, very impressive, 728 of these! The research problems do contain indeed structure questions that have not been solved today; a real toolkit for investigations. As before, in respect to the five volumes earlier in time, the authors did a formidable job. Some people did think, that with the classification of the finite simple groups, the subject of studying finite group theory came to end; only looking at the constants of the six volumes reveals already, that this opinion is totally wrong! Well, will there be a Volume 7? Time will tell. The six books constitute a fundamental source in learning and studying finite \(p\)-groups.