A finite group presentation with cyclically reduced symmetrized relators is a Dehn presentation if every nonempty freely reduced null word contains a relator segment longer than half that relator. Replacing the segment by the inverse complementary segment strictly shortens the word. Finiteness of both the alphabet and the relator set is part of this definition; merely permitting all null words as an infinite relator set would make the shortening property vacuous as a finiteness criterion.
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