A property of alternating groups

2003/03/04 by Henry Cejtin, Cejtin, Henry, Igor Rivin +1
Mathematics · #20B35 #20B40 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20B35 #msc:20B40

paper · pdf · doi:10.48550/arxiv.math/0303036

arxiv created 2003/03/18 · arxiv updated 2009/11/30

Abstract

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.

Related

• Generating alternating and symmetric groups with two elements of fixed\n order
• Commutators of n-cycles in the symmetric group
• Products of conjugacy classes of the alternating group
• A Survey of Alternating Permutations
• Generalization of the basis theorem for alternating groups