Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Some results on parafree groups

Author: Yael Roitberg
Journal: Trans. Amer. Math. Soc. 173 (1972), 315-339
MSC: Primary 20E10
MathSciNet review: 0313399
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We obtain some theorems concerning parafree groups in certain varieties, which are analogs of corresponding theorems about free groups in these varieties. Our principal results are: (1) A normal subgroup $ N$ of a parafree metabelian group $ P$ of rank $ \geqslant 2$ such that $ N \cdot {\gamma _2}P$ has infinite index in $ P$ is not finitely generated unless it is trivial. (2) If $ x$ and $ y$ are elements of a parafree group $ P$ in any variety containing the variety of all metabelian groups which are independent modulo $ {\gamma _2}P$, then the commutator $ [x,y]$ is not a proper power.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20E10

Retrieve articles in all journals with MSC: 20E10

Additional Information

Keywords: Parafree groups, varieties of groups, metabelian groups, lower central series, residually nilpotent groups, parabasis, left normed basic commutators
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society