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)



Representations of free metabelian $ \mathcal{D}_\pi$-groups

Author: John F. Ledlie
Journal: Trans. Amer. Math. Soc. 153 (1971), 307-346
MSC: Primary 20.40
MathSciNet review: 0276341
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For $ \pi $ a set of primes, a $ {\mathcal{D}_\pi }$-group is a group $ G$ with the property that, for every element $ g$ in $ G$ and every prime $ p$ in $ \pi ,g$ has a unique $ p$th root in $ G$. Two faithful representations of free metabelian $ {\mathcal{D}_\pi }$-groups are established: the first representation is inside a suitable power series algebra and shows that free metabelian $ {\mathcal{D}_\pi }$-groups are residually torsion-free nilpotent; the second is in terms of two-by-two matrices and is analogous to W. Magnus' representation of free metabelian groups using two-by-two matrices. In a subsequent paper [12], these representations will be used to derive several properties of free metabelian $ {\mathcal{D}_\pi }$-groups.

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20.40

Retrieve articles in all journals with MSC: 20.40

Additional Information

Keywords: Metabelian group, $ \mathcal{D}$-group, unique roots, power series algebra representation, matrix representation
Article copyright: © Copyright 1971 American Mathematical Society