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2011•journal of Groups complexity cryptologyRequires access

Polynomial time conjugacy in wreath products and free solvable groups

Svetla Vassileva

Open publisher page 19 citations

Abstract

We prove that the complexity of the conjugacy problems for wreath products and for free solvable groups is decidable in polynomial time. For the wreath product A wr B , we must assume the decidability in polynomial time of the conjugacy problems for A and B and of the power problem in B . Using this result and properties of the Magnus embedding, we show that the conjugacy and conjugacy search problems in free solvable groups are computable in polynomial time.

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What this paper is about

We prove that the complexity of the conjugacy problems for wreath products and for free solvable groups is decidable in polynomial time. For the wreath product A wr B , we must assume the decidability in polynomial time of the conjugacy problems for A and B and of the power problem in B . Using this result and properties of the Magnus embedding, we show that the conjugacy and conjugacy search problems in free solvable groups are computable in polynomial time.

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OpenAlex reports 19 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We prove that the complexity of the conjugacy problems for wreath products and for free solvable groups is decidable in polynomial time. For the wreath product A wr B , we must assume the decidability in polynomial time of the conjugacy problems for A and B and of the power problem in B . Using this result and properties of the Magnus embedding, we show that the conjugacy and conjugacy search problems in free solvable groups are computable in polynomial time.

Key concepts: Wreath product, Conjugacy problem, Mathematics, Conjugacy class, Solvable group, Decidability, Combinatorics, Embedding

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