Action in form of conjugation

Action in form of conjugation

In [8] it is shown that the ideas for computing orbit representatives under the group action in form of () can be generalized for group actions in form of (). You also have to compute the Sims-chain for the group action _GX. For finding short cuts in the minimality test the following two facts are important:

Let f<(p_j⁽ⁱ⁾)^-1 o f o p_j⁽ⁱ⁾, and let f(i)<( (p_j⁽ⁱ⁾)^-1 o f o p_j⁽ⁱ⁾)(i). If furthermore f(j)£i-1 for all j£i-1 and f(i)£i, then f<C_G(i)((p_j⁽ⁱ⁾)^-1 o f o p_j⁽ⁱ⁾).
If f£C_G(i)(f), and if there is some sÎC_G(i) such that s o (p_j⁽ⁱ⁾)^-1 o f o p_j⁽ⁱ⁾ o s^-1=f, then C_G(i)((p_j⁽ⁱ⁾)^-1 o f o p_j⁽ⁱ⁾) ³f.

harald.fripertinger@kfunigraz.ac.at,
last changed: January 23, 2001

Action in form of conjugation