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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
A Reversibility Characterization of Locally Finite Groups by Cellular Automata
Jiang Yang
For cellular automata over finite alphabets, bijectivity already implies reversibility. Over infinite alphabets this implication may fail, and the remaining obstruction in the peri…