Characterization of finitely generated groups by types

A. G. Myasnikov, N. S. Romanovskii

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование

2 Цитирования (Scopus)

Аннотация

In this paper we show that all finitely generated nilpotent, metabelian, polycyclic, and rigid (hence free solvable) groups G are fully characterized in the class of all groups by the set tp(G) of types realized in G. Furthermore, it turns out that these groups G are fully characterized already by some particular rather restricted fragments of the types from tp(G). In particular, every finitely generated nilpotent group is completely defined by its +-types, while a finitely generated rigid group is completely defined by its types, and a finitely generated metabelian or polycyclic group is completely defined by its -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.

Язык оригиналаанглийский
Страницы (с-по)1613-1632
Число страниц20
ЖурналInternational Journal of Algebra and Computation
Том28
Номер выпуска8
DOI
СостояниеОпубликовано - 1 дек 2018

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