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In particular, every finitely generated nilpotent group is completely defined by its [Formula: see text]-types, while a finitely generated rigid group is completely defined by its [Formula: see text]-types, and a finitely generated metabelian or polycyclic group is completely defined by its [Formula: see text]-types. We have similar results for some non-solvable groups: free, surface, and free Burnside groups, though they mostly serve as illustrations of general techniques or provide some counterexamples.<\/jats:p>","DOI":"10.1142\/s0218196718400118","type":"journal-article","created":{"date-parts":[[2018,9,7]],"date-time":"2018-09-07T01:39:38Z","timestamp":1536284378000},"page":"1613-1632","source":"Crossref","is-referenced-by-count":5,"title":["Characterization of finitely generated groups by types"],"prefix":"10.1142","volume":"28","author":[{"given":"A. 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