[GAP Forum] A question about involutions

[Alexander Hulpke]

Dear Forum, 

Fatemeh Moftakhar asked:

> I have a question.
> G is a graph and x is an involution in G. Is there any algorithm in GAP for
> computing the number of involutions in x^G such that O(xy) is odd?
> 
> Any comments or suggestions will be highly appreciated.

There is no direct function for this.

Assuming you mean G is a group, and it is small enough that you can calculate the character table, the class structure constants (see manual: 
ClassStructureCharTable, http://www.gap-system.org/Manuals/doc/ref/chap71.html#X7F9D58208241D35E        )
allow to determine such a count.

Regards,

  Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke