Author |
Topic: Sequences and Subgroups (Read 653 times) |
|
ecoist
Senior Riddler
Gender: 
Posts: 405
|
 |
Sequences and Subgroups
« on: Jun 11th, 2006, 8:02pm » |
 Quote  Modify
|
When Hans Zassenhaus was only 18, he wrote a book on group theory which contains the exercise
Let G be a group of order n. Show that, given any sequence x1,...,xn, of elements of G of length n, some consecutive subsequence, xi,...,xj, 1<=i<=j<=n, has product xi...xj equal to the identity of G.
What about the converse?
Let G be a group containing an n-subset H with the property that, for every sequence of elements of H of length n, some consecutive subsequence has product equal to the identity of G. Must H be a subgroup of G?
|
|
 IP Logged |
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print