MathDB

elements of n-th symmetric group

Source: 4-th Hungary-Israel Binational Mathematical Competition 1993

May 26, 2007

group theoryabstract algebrafunctionsuperior algebrasuperior algebra unsolved

Problem Statement

In the questions below:

G

is a ﬁnite group;

H \leq G

a subgroup of

G; |G : H |

the index of

H

in

G; |X |

the number of elements of

X \subseteq G; Z (G)

the center of

G; G'

the commutator subgroup of

H

the normalizer of

H

in

G; C_{G}(H )

the centralizer of

H

in

G

; and

S_{n}

the

n

-th symmetric group. Show that every element of

S_{n}

is a product of

2

-cycles.

Back to Problems View on AoPS