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Reflections on discriminating groups
-
Gilbert Baumslag
and
Dennis Spellman
Published/Copyright:
February 12, 2007
Abstract
Here we continue the study of discriminating groups as introduced by Baumslag, Myasnikov and Remeslennikov in [G. Baumslag, A. G. Myasnikov and V. N. Remeslennikov. Discriminating and codiscriminating groups. J. Group Theory3 (2000), 467–479.]. First we give examples of finitely generated groups which are discriminating but not trivially discriminating, in the sense that they do not embed their direct squares, and then we show how to generalize these examples. In the opposite direction we show that if F is a non-abelian free group and R is a normal subgroup of F such that F/R is torsion-free, then F/R′ is non-discriminating.
Received: 2004-07-19
Revised: 2006-01-11
Published Online: 2007-02-12
Published in Print: 2007-01-26
© Walter de Gruyter
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Articles in the same Issue
- Finite 2-groups all of whose maximal cyclic subgroups of composite order are self-centralizing
- Maximal elementary abelian subgroups of rank 2
- A Morita equivalence for blocks of finite p-solvable groups in the Glauberman–Isaacs–Watanabe correspondence context
- A remark on the identification of Lie-type groups as amalgams of minimal parabolic subgroups
- A product decomposition for the classical quasisimple groups
- A natural invariant algebra for the Baby Monster group
- Recognition of the finite almost simple groups PGL2(q) by their spectrum
- Reflections on discriminating groups
- Pseudo-elementary generalized triangle groups
- Poly-free constructions for right-angled Artin groups
