On generalisations of conciseness
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- AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-117281GB-I00/ES/
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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, (m) ...,G] is finite for some m ∈ N if and only if [w(G), G] is finite.
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