JP Journal of Algebra, Number Theory and Applications
Volume 18, Issue 2, Pages 125 - 143
(September 2010)
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ROOT-CLASS RESIDUALITY OF SOME FREE CONSTRUCTIONS
D. Tieudjo
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Abstract: This is a survey of some recent results obtained on root-class residuality. First, we review and extend some properties of root-class residuality of generalized free products and HNN-extensions. Then conditions such that, by adjoining roots to a root-class residual group, the resulting group is again root-class residual, are derived. These results are extended to generalized free product of infinitely many groups amalgamating a common subgroup and also to multiple HNN-extensions. Further, they are applied to study root-class residuality of some one-relator groups. |
Keywords and phrases: root-class, root-class residuality, root-class separability, generalized free product, HNN-extensions. |
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