For a group and an element, the order of is the smallest natural number such that the -fold group product of with itself is the neutral element:
Of a group scheme
Sometimes the term ”order” refers to the height of a (group) scheme over a field (of characteristic ) which is defined to be the dimension of the associated ring of functions as a -vector space. Another term for this notion is ”rank”. If this group scheme is moreover p-divisible - which means that is is in fact a codirected diagram of group schemes of order ; in this case is called the order or height of .
Revised on October 17, 2012 13:40:57
by Urs Schreiber