A property of alternating groups

doi:https://doi.org/10.48550/arxiv.math/0303036

Open AccessPreprint10.48550/arxiv.math/0303036

A property of alternating groups

Henry Cejtin,Igor Rivin-2003-03-04-ArXiv.org

TL;DRAbstract

We describe an efficient algorithm to write any element of the alternating group A_n as a product of two n-cycles (in particular, we show that any element of A_n can be so written -- a result of E. A. Bertram). An easy corollary is that every element of A_n is a commutator in the symmetric group S_n.

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We describe an efficient algorithm to write any element of the alternating group A_n as a product of two n-cycles (in particular, we show that any element of A_n can be so written -- a result of E. A. Bertram). An easy corollary is that every element of A_n is a commutator in the symmetric group S_n.

Keywords

CorollaryElement (criminal law)Property (philosophy)Group (periodic table)Product (mathematics)CommutatorMathematicsAlternating group

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