Dear Friends, I am writing a GAP code to find whether certain subgroup properties are preserved under direct products in finite groups. But it seems that Direct product of groups in GAP has some different setting. For instance, If we D= DirectProduct(A_4,S_3); where A_4 is the alternating group of order 12 and S_3 is the symmetric group in three letters; and if w1=the identity subgroup in A_4 w2=the subgroup of order 3 in S3 W=DirectProduct(w1,w2) Then GAP recognize W as subgroup in D, GAP recognize W as non-normal subgroup. What is wrong here? and how get the elements of the direct product group as ordered pairs in GAP. Thank you.
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