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math.GR2026
Residual profiles and bounded generation in pro- completions of amalgamated products
Dekui Peng, Jiang Yang
This paper completely classifies when the pro- completion of an amalgamated product has bounded generation, assuming its starting vertex groups are already boundedly generated.…
math.GR2026
Shadowing and Hyperbolicity for Endomorphisms of Locally Compact Groups
Dekui Peng
We study shadowing, with respect to the left uniformity, for continuous endomorphisms of Lie groups and totally disconnected locally compact groups. For Lie groups, an endomorphism…
math.GR2026
Remarks on -independent topological groups
Zhouxiang Huang, Dekui Peng, Gao Zhang
A non-trivial topological group is called \emph{-independent} if for every subgroup of cardinality less than the continuum there exists a countable dense subgroup intersecting i…