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1993•Proceedings of the American Mathematical SocietyRequires access

The Length of Elements in Free Solvable Groups

Carl Droms, Jacques Lewin, Herman Servatius

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Abstract

We examine the relationship between the complexity of the word problem for a presentation and the complexity of the problem of determining the length of a shortest word equivalent to a given word. Our main result is that the length of the element represented by a word in a free solvable group can be determined in polynomial time.

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What this paper is about

We examine the relationship between the complexity of the word problem for a presentation and the complexity of the problem of determining the length of a shortest word equivalent to a given word. Our main result is that the length of the element represented by a word in a free solvable group can be determined in polynomial time.

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OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We examine the relationship between the complexity of the word problem for a presentation and the complexity of the problem of determining the length of a shortest word equivalent to a given word. Our main result is that the length of the element represented by a word in a free solvable group can be determined in polynomial time.

Key concepts: Word (group theory), Word problem (mathematics education), Word length, Presentation (obstetrics), Mathematics, Element (criminal law), Polynomial, Combinatorics

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