2025/08/09 by Zozaya, Andoni
#20F10 #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2508.07012
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 but not concise. We further establish that every 1/m-concise word is semiconcise by proving that when the group word w takes finitely many values in G, the iterated commutator subgroup [w(G), G, \stackrel(m)…, G] is finite for some m ∈ ℕ if and only if [w(G), G] is finite.