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Combinatorics of Permutations, 2nd Edition
book

Combinatorics of Permutations, 2nd Edition

by Miklos Bona
April 2016
Intermediate to advanced content levelIntermediate to advanced
478 pages
14h 44m
English
Chapman and Hall/CRC
Content preview from Combinatorics of Permutations, 2nd Edition
90 Combinatorics of Permutations, Second Edition
PROPOSITION 3.9
The set of all even permutations in S
n
forms a subgroup.
This subgroup is called the alternating group of degree n, and is denoted
by A
n
. The reader should prove at this point that A
n
has n!/2 elements if
n 2, then she should check her answer in Exercise 1. Like the symmetric
group, the alternating group has been vigorously investigated throughout the
last century. For instance, it is known that A
n
is a simple group if n 5. In
fact, among all finite simple groups, A
n
is the easiest to define, except for the
cyclic groups Z
p
,wherep is a prime. (See any introductory book on group
theory for the definition of a simple group or Z
p
.) It is also interesting that A
n
is by far larger than any other ...
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Publisher Resources

ISBN: 9781439850527