[GAP Forum] "generalized centralizer question

Walter Becker w_becker at hotmail.com
Tue Jul 15 18:13:10 BST 2008

I am interested in calculating the set of elements (group) which commute with a given non-abelian subgroup of a group. 
The problem can be illustrated by a simple example.
Consider the group 
[C_(9} @ C_3] @ D_4 = G
The group D_4 acts on the 3-group by an operator of order 2 (say here the C_2 element in D_4).  What I want to do is to calculate the "normal subgroup" [C_9 @ C_3 X C_4] and then form the quotient group 
Q = G/[C_9 at C_3 X C_4]
Here the quotient is obviously C_2. But the interest is in more general cases with a non-abelian normal p-subgroup. (The case when the p-group is abelian can be done with the centralizer command.)
Thank you
Walter Becker
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