Question

find the direct product of S3 and A3?​

Answer 1

Answer:

SA9

Step-by-step explanation:

S3×A3=A×S×3×3

=SA9

Answer 2

The direct product of S3 and A3 is 18 elements.

Step-by-step explanation:

DirectProduct( s3, a3 );

Group([ (1,2), (1,2,3), (4,5,6) ])

Order( s3a3 )

= 18  elements

(If we had defined a3s3:= DirectProduct( a3, s3 )

The result would have been

Group([ (1,2,3), (4,5), (4,5,6) ]), which is, of course, isomorphic to s3a3.)

So the direct product group $s3 a3 : = S3 \times A 3 ,$, which has $|S 3| \cdot|A 3|=18$ elements.