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math.GR2025
Flexible -valent graphs of even girth
Marco Barbieri, Andoni Zozaya
We prove the existence of a connected flexible -valent vertex-transitive graph of girth for every integer . We also give a constructive proof if is prime.
math.GR2025
On generalisations of conciseness
Andoni Zozaya
Based on the notions of conciseness and semiconciseness, we show that these properties are not equivalent by proving that a word originally presented by Ol'shanskii is semiconcise…
math.GR2025
Strong conciseness and equationally Noetherian groups
Iker de las Heras, Andoni Zozaya
A word is said to be concise in a class of groups if, for every in that class such that the set of -values is finite, the verbal subgroup is also finite.…