Characterization of solvable groups and solvable radical. (Q2852572)

This survey of 51 pages and 161 references contains some fundamental discussions and recent characterisations about finite solvable groups. It is impossible to list here all the details, which go from some old classical conjectures to new and intriguing perspectives of study. The main motivation of this survey is due to the results obtained by Professor Grunewald and his coauthors in the last decades. There are so many deep ideas, open questions, and relations with various branches of pure mathematics that I think that the best way to review this contribution is to refer directly to the introduction from page 1013 to page 1014. From these two pages, in my humble opinion, it is clear that the quantity and the quality of the mathematics, which is contained in the survey, will offer a valid source of inspiration for the research on the topic of the next years.