This preview shows page 1. Sign up to view the full content.
Unformatted text preview: S 4 which commute with (1 2)(3 4). Let n Z + and let g A n . Suppose 4n and  g  2. Considering A n as acting on { 1 , . . . , n } , prove that gi = i for some i where 1 i n . Since the order of g is 1 or 2, when we write it as a product of disjoint cycles, only 2cycles can occur (and 1cycles, which may be omitted). Suppose g has no xed points (i.e. no such i exists). Then g must be a product of n / 2 disjoint 2cycles. Since n / 2 must be an integer and 4n , we deduce that g is a product of an odd number of transpositions. This contradicts the fact that g A n ....
View Full
Document
 Fall '07
 PALinnell
 Math, Algebra

Click to edit the document details