Nilpotency class: Difference between revisions
No edit summary |
|||
| Line 9: | Line 9: | ||
* It is the length of the [[upper central series]] | * It is the length of the [[upper central series]] | ||
* It is the length of the [[lower central series]] | * It is the length of the [[lower central series]] | ||
* It is the length of | * It is the minimum possible length of a central series | ||
A group is said to be of class <math>c</math> if its nilpotence class is less than or equal to <math>c</math>. | A group is said to be of class <math>c</math> if its nilpotence class is less than or equal to <math>c</math>. | ||
Revision as of 13:14, 2 July 2008
This article defines an arithmetic function on a restricted class of groups, namely: nilpotent groups
Definition
Symbol-free definition
For a nilpotent group, the nilpotency class or nilpotence class is defined in any of the following equivalent ways:
- It is the length of the upper central series
- It is the length of the lower central series
- It is the minimum possible length of a central series
A group is said to be of class if its nilpotence class is less than or equal to .
Equivalence of definitions
For full proof, refer: Equivalence of definitions of nilpotency class