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NottinghamGroup examples
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If F is a finite field with p  elements, then we may form the group
of all formal power series {t(1+a t+a t+...)} where u(0)=0 and 
 ,                               1   2
u (0)=1 and $a is an element of F. 
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The group operation is substitution (composition).
This is called the Nottingham Group. 

The Nottingham Group is the projective limit of finite p-groups.
Every finite p-group can be embedded in the Nottingham Group.

   x:=monomial(1,1)$UFPS PF 1783
     x

   s:=retract(sin x)$NOTTING PF 1783
             3        5       7       9      11
     x + 297x  + 1679x  + 427x  + 316x  + O(x  )

   s^2
             3       5        7        9      11
     x + 594x  + 535x  + 1166x  + 1379x  + O(x  )

   s^-1
              3       5       7        9      11
     x + 1486x  + 847x  + 207x  + 1701x  + O(x  )

   s^-1*s
            11
     x + O(x  )

   s*s^-1
               11
        x + O(x  )

See Also:
o )show NottinghamGroup
o )show UnivariateFormalPowerSeries

