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Power-Commutative Nilpotent R-Powered Groups
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Stephen Majewicz
Published/Copyright:
March 10, 2010
If R is a binomial ring, then a nilpotent R-powered group G is termed power-commutative if for any α ∈ R, [gα, h] = 1 implies [g, h] = 1 whenever gα ≠ 1. In this paper, we further contribute to the theory of nilpotent R-powered groups. In particular, we prove that if G is a nilpotent R-powered group of finite type which is not of finite π-type for any prime π ∈ R, then G is PC if and only if it is an abelian R-group.
Keywords:: Nilpotent R-powered group; R-powered group; nilpotent R-group; finite type; power-commutative; PC-group
Received: 2009-03-19
Revised: 2009-06-30
Published Online: 2010-03-10
Published in Print: 2009-October
© Heldermann Verlag
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Keywords for this article
Nilpotent R-powered group;
R-powered group;
nilpotent R-group;
finite type;
power-commutative;
PC-group
Articles in the same Issue
- The Word and Conjugacy Problem for Shuffle Groups
- Torsion-free Abelian Factor Groups of the Baumslag-Solitar Groups and Subgroups of the Additive Group of the Rational Numbers
- Metabelian Product of a Free Nilpotent Group with a Free Abelian Group
- Almost Locally Free Groups and a Theorem of Magnus: Some Questions
- Authentication from Matrix Conjugation
- The Tits Alternative for Tsaranov's Generalized Tetrahedron Groups
- Decision and Search in Non-Abelian Cramer-Shoup Public Key Cryptosystem
- A Note on the Shifted Conjugacy Problem in Braid Groups
- Algebraic Attacks Galore!
- Space Complexity and Word Problems of Groups
- A Practical Attack on a Certain Braid Group Based Shifted Conjugacy Authentication Protocol
- Existence and Non-Existence of Torsion in Maximal Arithmetic Fuchsian Groups
- Power-Commutative Nilpotent R-Powered Groups
- On the Universal Theory of Torsion and Lacunary Hyperbolic Groups
